Chapter 4 The rabbit population in a forest area grows at the rate

Ch.4 ExponentialandLogarithmicFunctions

4.1 ExponentialFunctions

1 EvaluateExponentialFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Approximatethenumberusingacalculator.Roundyouranswertothreedecimalplaces.

1) 21.7

A) 3.249 B) 3.400 C) 2.890 D) 3.549

2) 2–3.3

A) 0.102 B) –6.600 C) 10.890 D) 0.402

3) 2 7

A) 6.258 B) 5.292 C) 7.000 D) 64.000

4) 2.4π

A) 15.648 B) 15.601 C) 7.540 D) 36.462

Solvetheproblem.

5) Thefunctionf(x)=600(0.5)x/80modelstheamountinpoundsofaparticularradioactivematerialstoredina

concretevault,wherexisthenumberofyearssincethematerialwasputintothevault.Findtheamountof

radioactivematerialinthevaultafter140years.Roundtothenearestwholenumber.

A) 178pounds B) 404pounds C) 525 pounds D) 171 pounds

6) Therabbitpopulationinaforestareagrowsattherateof5%monthly.Ifthereare150rabbitsinSeptember

,

findhowmanyrabbits(roundedtothenearestwholenumber)shouldbeexpectedbynextSeptember.Use

y=150(2.7)0.05t.

A) 272 B) 243 C) 285 D) 259

7) Acityisgrowingattherateof0.9%annually.Iftherewere3,619,000 residentsinthecityin1994

,

findhow

many(tothenearestten–thousand)arelivinginthatcityin2000.Usey=3,619,000(2.7)0.009t.

A) 3,820,000 B) 530,000 C) 9,770,000 D) 3,850,000

8) TheformulaS=A(1+r)t+1–1

rmodelsthevalueofaretirementaccount,whereA=thenumberofdollars

addedtotheretirementaccounteachyear,r=theannualinterestrate,andS=thevalueoftheretirement

accountaftertyears.Iftheinterestrateis6%,howmuchwilltheaccountbeworthafter10yearsif$1600is

addedeachyear?Roundtothenearestwholenumber.

A) $23,955 B) $3021 C) $17,600 D) $31,519

Page1

2 GraphExponentialFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Graphthefunctionbymakingatableofcoordinates.

1) f(x)=4x

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page2

2) f(x)=1

3

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page3

3) f(x)=4

3

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page4

4) f(x)=0.3x



x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page5

Thegraphofanexponentialfunctionisgiven.Selectthefunctionforthegraphfromthefunctionslisted.

5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=2xB) f(x)=2x+1C) f(x)=2x+1 D) f(x)=2x–1

6)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=3x–1B) f(x)=3xC) f(x)=3x–1 D) f(x)=3x+1

7)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=3x–2 B) f(x)=3xC) f(x)=3x–2D) f(x)=3x+2

Page6

8)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=–3xB) f(x)=3xC) f(x)=3–xD) f(x)=–3–x

9)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=2–xB) f(x)=2xC) f(x)=–2xD) f(x)=–2–x

10)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=–3–xB) f(x)=3xC) f(x)=–3xD) f(x)=3–x

Page7

Graphthefunction.

11) Usethegraphoff(x)=2xtoobtainthegraphofg(x)=2x–3.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page8

12) Usethegraphoff(x)=2xtoobtainthegraphofg(x)=2x–1.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page9

13) Usethegraphoff(x)=4xtoobtainthegraphofg(x)=4x+3+2.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page10

14) Usethegraphoff(x)=4xtoobtainthegraphofg(x)=4–x.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page11

15) Usethegraphoff(x)=2xtoobtainthegraphofg(x)=–2x.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page12

16) Usethegraphoff(x)=4xtoobtainthegraphofg(x)=1

4·4x.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page13

17) Usethegraphoff(x)=4xtoobtainthegraphofg(x)=4·4x.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page14

18) Usethegraphoff(x)=extoobtainthegraphofg(x)=e6x.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page15

19) Usethegraphoff(x)=extoobtainthegraphofg(x)=ex+3.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page16

20) Usethegraphoff(x)=extoobtainthegraphofg(x)=2ex.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page17

21) Usethegraphoff(x)=extoobtainthegraphofg(x)=ex–2.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page18

22) Usethegraphoff(x)=extoobtainthegraphofg(x)=ex–3+1.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page19

23) Usethegraphoff(x)=extoobtainthegraphofg(x)=e–x.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page20

24) Usethegraphoff(x)=extoobtainthegraphofg(x)=–ex.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page21

25) Usethegraphoff(x)=extoobtainthegraphofg(x)=1

2ex.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

-8

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

-8

Page22

26) Usethegraphoff(x)=extoobtainthegraphofg(x)=ex/2–1.

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

-8

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

-8

3 EvaluateFunctionswithBasee

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Approximatethenumberusingacalculator.Roundyouranswertothreedecimalplaces.

1) e1.1

A) 3.004 B) 2.990 C) 1.296 D) 3.304

2) e–0.6

A) 0.549 B) –1.631 C) –0.549 D) 0.849

Page23

Solvetheproblem.

3) Thesizeoftheraccoonpopulationatanationalparkincreasesattherateof4.9%peryear.Ifthesizeofthe

currentpopulationis155,findhowmanyraccoonsthereshouldbein8years.Usethefunction

f(x)=155e0.049tandroundtothenearestwholenumber.

A) 229 B) 231 C) 227 D) 233

4) Thepopulationinaparticularcountryisgrowingattherateof1.5%peryear.If6,365,000peoplelivedtherein

1999,howmanywilltherebeintheyear2003?Usef(x)=y0e0.015tandroundtothenearestten–thousand.

A) 6,760,000 B) 7,430,000 C) 6,620,000 D) 8,110,000

5) ThefunctionD(h)=7e–0.4hcanbeusedtodeterminethemilligramsDofacertaindruginapatientʹs

bloodstreamhhoursafterthedrughasbeengiven.Howmanymilligrams(totwodecimals)willbepresent

after12hours?

A) 0.06mg B) 850.57 mg C) 4.16 mg D) 0.73 mg

6) Asampleof500goflead–210decaystopolonium–210accordingtothefunctiongivenbyA(t)=500e–0.032t,

wheretistimeinyears.Whatistheamountofthesampleafter60years(tothenearestg)?

A) 73g B) 3410 g C) 121 gD)53g

4 UseCompoundInterestFormulas

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

UsethecompoundinterestformulasA=P1+

r

n

ntandA=Perttosolve.

1) Findtheaccumulatedvalueofaninvestmentof$9000 at5%compoundedannuallyfor6years.

A) $12,060.86 B) $11,486.53 C) $11,250.00 D) $11,700.00

2) Findtheaccumulatedvalueofaninvestmentof$6000 at4%compoundedsemiannuallyfor8years.

A) $8236.71 B) $8211.41 C) $7029.96 D) $7920.00

3) Findtheaccumulatedvalueofaninvestmentof$1000 at12%compoundedquarterlyfor3years.

A) $1425.76 B) $1404.93 C) $1092.73 D) $1360.00

4) Findtheaccumulatedvalueofaninvestmentof$770 at3%compoundedannuallyfor16years.

A) $1235.62 B) $1199.63 C) $1116.50 D) $1139.60

5) Findtheaccumulatedvalueofaninvestmentof$2000 at8%compoundedcontinuouslyfor4years.

A) $2754.26 B) $2854.26 C) $2720.98 D) $2640.00

6) Findtheaccumulatedvalueofaninvestmentof$5000at5%compoundedmonthlyfor8years.

A) $7452.93 B) $12,911.25 C) $9093.60 D) $8060.16

7) Supposethatyouhave$3000toinvest.Whichinvestmentyieldsthegreaterreturnover10years:8.75%

compoundedcontinuouslyor8.9%compoundedsemiannually?

A) $3000investedat8.75%compoundedcontinuouslyover10 yearsyieldsthegreaterreturn.

B) $3000investedat8.9%compoundedsemiannuallyover10 yearsyieldsthegreaterreturn.

C) Bothinvestmentplansyieldthesamereturn.

Page24

8) Supposethatyouhave$5000toinvest.Whichinvestmentyieldsthegreaterreturnover8years:5.4%

compoundedmonthlyor5.5%compoundedquarterly?

A) $5000investedat5.5%compoundedquarterlyover8 yearsyieldsthegreaterreturn.

B) $5000investedat5.4%compoundedmonthlyover8 yearsyieldsthegreaterreturn.

C) Bothinvestmentplansyieldthesamereturn.

4.2 LogarithmicFunctions

1 ChangefromLogarithmictoExponentialForm

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Writetheequationinitsequivalentexponentialform.

1) log 525=2

A) 52=25 B) 25=25 C) 525=2D)25

2=5

2) log 5x=2

A) 52=xB)2

5=xC)5

x=2D)x

2=5

3) log

b

64=3

A) b3=64 B) 3

b

=64 C) 643=bD)64

b

=3

4) log 24=x

A) 2x=4B)x

2=4C)4

x=2D)4

2=x

2 ChangeFromExponentialtoLogarithmicForm

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Writetheequationinitsequivalentlogarithmicform.

1) 63=216

A) log 6216=3 B) log 216 6=3 C) log 3216 =6 D) log 63=216

2) 3–2=1

9

A) log 31

9=–2 B) log 1/3 3=–2 C) log –2

1

9=3 D) log 3–2=1

9

3) 73=x

A) log 7x=3 B) log x7=3 C) log 3x=7 D) log 73=x

4) 364=4

A) log 64 4=1

3B) log 464=1

3C) log 64 3=1

4D) log 464 =3

5) 43=y

A) log 4y=3 B) log 3y=4 C) log y4=3 D) log y3=4

6) c3=512

A) logc512=3 B) log512 c=3 C) log3512 =c D) logc3=512

Page25

7) 10x=1000

A) log 10 1000=x B) log x1000 =10 C) log 1000 10 =x D) log 1000 x=10

3 EvaluateLogarithms

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Evaluatetheexpressionwithoutusingacalculator.

1) log 5125

A) 3 B) 15 C) 1

3D) 1

2) log 10 10,000

A) 4 B) 40 C) 1

10000 D) –4

3) log9729

A) 3 B) 729 C) 27 D) 9

4) log 11 11

A) 1

2B) 11 C) 1

11 D) 1

5) log 4

1

64

A) –3B)12C)

1

3D) 3

6) log 82

A) 1

3B) 6 C) 3 D) 1

7) log21

2

A) –1B)2 C)

–2D)1

8) log31

3

A) –1

2B) 1

2C) 1

3D) –1

3

4 UseBasicLogarithmicProperties

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Evaluatetheexpressionwithoutusingacalculator.

1) log 51

A) 0 B) 5 C) 1

5D) 1

Page26

2) log 12 12

A) 1 B) 12 C) 1

12 D) 0

3) 5 log 514

A) 14 B) 5 C) 19 D) log 514

4) log 3319

A) 19 B) 3 C) 22 D) log 319

5 GraphLogarithmicFunctions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Thegraphofalogarithmicfunctionisgiven.Selectthefunctionforthegraphfromtheoptions.

1)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=log 4x B) f(x)=log 4(x–2) C) f(x)=log 4(x+2) D) f(x)=log 4x–2

2)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=log 5(x+2) B) f(x)=log 5x C) f(x)=log 5(x–2) D) f(x)=log 5x+2

Page27

3)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=log 5x+1 B) f(x)=log 5x C) f(x)=log 5(x–1) D) f(x)=log 5(x+1)

4)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=log 4(–x) B) f(x)= – log 4x C) f(x)=1–log 4x D) f(x)=log 4x

5)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=–log 3x B) f(x)=log 3(–x) C) f(x)=1–log 3x D) f(x)=log 3x

Page28

6)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A) f(x)=1–log 4x B) f(x)=log 4(–x) C) f(x)= – log 4x D) f(x)=log 4x

Page29

Graphthefunction.

7) Usethegraphoflog 5xtoobtainthegraphoff(x)=log 5(x+2).

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page30

8) Usethegraphoflog 5xtoobtainthegraphoff(x)=1+log 5x.

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page31

9) Usethegraphoflog 4xtoobtainthegraphoff(x)=2 log 4x.

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page32

10) Usethegraphoflog 5xtoobtainthegraphoff(x)=1

2log 5x.

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page33

Graphthefunctionsinthesamerectangularcoordinatesystem.

11) f(x)=5xandg(x)=log5x

x

-6 6

y

6

-6

x

-6 6

y

6

-6

A)

x

-6 6

y

6

-6

x

-6 6

y

6

-6

B)

x

-6 6

y

6

-6

x

-6 6

y

6

-6

C)

x

-6 6

y

6

-6

x

-6 6

y

6

-6

D)

x

-6 6

y

6

-6

x

-6 6

y

6

-6

Page34

12) f(x)=1

4

xandg(x)=log1/4x

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

A)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

B)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

C)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

D)

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

x

-6 -4 -2 2 4 6

y

6

4

2

-2

-4

-6

Page35

Graphthefunction.

13) Usethegraphoff(x)=logxtoobtainthegraphofg(x)=log(x+4).

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page36

14) Usethegraphoff(x)=logxtoobtainthegraphofg(x)=logx+4.

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page37

15) Usethegraphoff(x)=logxtoobtainthegraphofg(x)=3–logx.

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

A)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

B)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

C)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

D)

x

-10 -5 5 10

y

10

5

-5

-10

x

-10 -5 5 10

y

10

5

-5

-10

Page38

16) Usethegraphoff(x)=lnxtoobtainthegraphofg(x)=3 lnx.

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

Page39

17) Usethegraphoff(x)=lnxtoobtainthegraphofg(x)= –3–lnx.

x

-5 5

y

5

-5

x

-5 5

y

5

-5

A)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

B)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

C)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

D)

x

-5 5

y

5

-5

x

-5 5

y

5

-5

6 FindtheDomainofaLogarithmicFunction

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Findthedomainofthelogarithmicfunction.

1) f(x)=log 6(x+9)

A) (–9

,

∞)B)(6

,

∞)C)(9

,

∞)D)(

–∞

,

0)or(0,∞)

2) f(x)=log 3(x–8)

A) (8

,

∞)B)(

–∞

,

8)or(8

,

∞)C)(

–8

,

∞)D)(

–∞

,

0)or(0,∞)

3) f(x)=ln(4–x)

A) (–∞

,

4) B) (–∞

,

0) C) (–4

,

∞)D)(

–∞

,

4)or(4

,

∞)

Page40

4) f(x)=log 3(x–2)2

A) (–∞

,

2)or(2

,

∞)B)(

–∞

,

0) or(0,∞)C)(

–2

,

∞)D)(2

,

∞)

5) f(x)=log 2(x+4)2

A) (–∞

,

–4)or(–4

,

∞)B)(

–∞

,

0) or(0,∞)C)(

–4

,

∞)D)(4

,

∞)

6) f(x)=log(x2–13x+36)

A) (–∞

,

4)∪(9

,

∞)B)(

–4

,

9) C) (9

,

∞)D)(

–∞

,

–4)

7) f(x)=logx+3

x–9

A) (–∞

,

–3)∪(9

,

∞)B)(

–3

,

9) C) (9

,

∞)D)(

–∞

,

–3)

8) f(x)=ln1

x+4

A) (–4

,

∞)B)(4

,

∞) C) (0,∞) D) (1,∞)

7 UseCommonLogarithms

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Evaluateorsimplifytheexpressionwithoutusingacalculator.

1) log10,000

A) 4 B) 1

4C) 2

5D) 40

2) log1

1000

A) –3B)3 C)1

1000 D) –1

3

3) log0.001

A) –3B)3 C)

–1

3D) 1

3

4) log106

A) 6 B) 10 C) log6D)10

6

5) 10log7

A) 7 B) 10,000,000 C) 70 D) 0.0000001

6) 9log109.8

A) 88.2 B) 882 C) 8.82 D) 20.5414

7) 6 10log9.3

A) 55.8 B) 558 C) 5.58 D) 13.3801

8) 10log5x

A) x1/5 B) x5C) 5 D) x–1/5

Page41

Solvetheproblem.

9) UsetheformulaR=loga

T+BtofindtheintensityRontheRichterscale,giventhatamplitudeais320

micrometers,timeTbetweenwavesis3.9seconds,andBis3.1.Roundanswertoonedecimalplace.

A) 5 B) 7.5 C) 1.9 D) 7.3

10) ThepHofasolutionrangesfrom0to14.AnacidhasapHlessthan7.PurewaterisneutralandhasapHof7.

ThepHofasolutionisgivenbypH=–logxwherexrepresentstheconcentrationofthehydrogenionsinthe

solutioninmolesperliter.FindthepHifthehydrogenionconcentrationis1x10–2.

A) 2 B) 12 C) –2D)

–12

11) ThepHofasolutionrangesfrom0to14.AnacidhasapHlessthan7.PurewaterisneutralandhasapHof7.

ThepHofasolutionisgivenbypH=–logxwherexrepresentstheconcentrationofthehydrogenionsinthe

solutioninmolesperliter.FindthepHifthehydrogenionconcentrationis2.8x10–3.

A) 2.55 B) 3.45 C) 3.55 D) 2.45

8 UseNaturalLogarithms

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Evaluateorsimplifytheexpressionwithoutusingacalculator.

1) lne2

A) 2 B) e C) 1

2D) 1

2) lne

A) 1 B) 0 C) e D) –1

3) ln1

A) 0 B) 1 C) e D) –1

4) ln6e

A) 1

6B) e

6C) 6 D) 6e

Evaluatetheexpressionwithoutusingacalculator.

5) ln1

e7

A) –7B)7 C)

1

7D) –1

7

6) eln271

A) 271 B) –271 C) e271 D) ln271

7) lne14x

A) 14x B) –14x C) e14x D) 1

14x

8) eln9x3

A) 9x3B) e9x3C) ln9x3D) 3

Page42

Solvetheproblem.

9) Thelongjumprecord,infeet,ataparticularschoolcanbemodeledbyf(x)=20.1+2.5ln(x+1) wherexisthe

numberofyearssincerecordsbegantobekeptattheschool.Whatistherecordforthelongjump 6yearsafter

recordstartedbeingkept?Roundyouranswertothenearesttenth.

A) 25.0feet B) 24.6 feet C) 24.1 feet D) 22.6 feet

10) Thefunctionf(x)=1+1.5ln(x+1)modelstheaveragenumberoffree–throwsabasketballplayercanmake

consecutivelyduringpracticeasafunctionoftime,wherexisthenumberofconsecutivedaysthebasketball

playerhaspracticedfortwohours.After206daysofpractice,whatistheaveragenumberofconsecutivefree

throwsthebasketballplayermakes?

A) 9consecutivefreethrows B) 10 consecutivefreethrows

C) 12consecutivefreethrows D) 13 consecutivefreethrows

4.3 PropertiesofLogarithms

1 UsetheProductRule

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usepropertiesoflogarithmstoexpandthelogarithmicexpressionasmuchaspossible.Wherepossible,evaluate

logarithmicexpressionswithoutusingacalculator.

1) log 6(7·3)

A) log 67+log 63 B) log 67–log 63 C) log 621 D) ( log 67)( log 63)

2) log 7(7x)

A) 1+log 7xB)7 C)x D)1

3) log 5(25x)

A) 2+log 5xB)10+log 5x C) 2x D) 2 log 5x

4) log(100x)

A) 2+logxB)20+logx C) 2x D) 2logx

2 UsetheQuotientRule

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usepropertiesoflogarithmstoexpandthelogarithmicexpressionasmuchaspossible.Wherepossible,evaluate

logarithmicexpressionswithoutusingacalculator.

1) log 3

7

13

A) log 37–log 313 B) log 37+log 313 C) log 313 –log 37D)

log 37

log 313

2) log 7

7

x

A) 1–log 7xB)7 C)

1

xD) –log 7x

3) logx

10

A) logx–1 B) logx+1C)

–10x D) 10x

Page43

4) log 2

8

x

A) 3–log 2xB)6–log 2xC)

3

xD) –3 log 2x

5) lne2

9

A) 2–ln9B)lne2–ln9C)2

+ln9D)lne2+ln9

3 UsethePowerRule

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usepropertiesoflogarithmstoexpandthelogarithmicexpressionasmuchaspossible.Wherepossible,evaluate

logarithmicexpressionswithoutusingacalculator.

1) lognx5

A) 5lognxB)

–5lognx C) nlog5xD)

–nlog5x

2) logX–2

A) –2logX B) 2logXC)

–2+logXD)2+logX

3) ln7x

A) 1

7lnxB)7lnx C) xln7D)7lnx

4) log 7x6

A) 6 log 7x B) 7 log 6xC)7logx D) 6 log 7x6

5) log 57–3

A) –3 log 57 B) 5 log 37C)

–15 log7 D) 7 log 53

6) log 8

3y

A) 1

3log 8yB)

1

8log 3yC)

1

3log 8

3yD) 3 log 8y

4 ExpandLogarithmicExpressions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usepropertiesoflogarithmstoexpandthelogarithmicexpressionasmuchaspossible.Wherepossible,evaluate

logarithmicexpressionswithoutusingacalculator.

1) logb(yz4)

A) logby+4logbzB)4logby+4 logbzC)4logbyz D) logby+logb4z

Page44

2) log 6

7·11

13

A) log 67+log 611–log 613 B) log 6(77

13 )

C) log 677–log 613 D) log 65

3) log 2

x2

y7

A) 2 log 2x–7 log 2y B) 2 log 2x+7 log 2yC)

2

7log 2(x

y) D) 7 log 2y–2 log 2x

4) log 6

x–6

x8

A) log 6(x–6)–8 log 6x B) log 6(x–6)+8 log 6x

C) 8 log 6x–log 6(x–6) D) log 6(x–6)–log 6x

5) log w

13x

2

A) log w13+log wx–log w2 B) log w11x

C) log w13x–log w2 D) log w13 +log wx+log w2

6) log 53x

A) 1

2log 53+1

2log 5x B) log 53+log 5x

C) 1

2log 53x D) log 53+1

2log 5x

7) log 5

x

125

A) 1

2log 5x–3B)15–1

2log 5x C) log 5x–3D)

–3 log 5x

8) ln3ey

A) 1

3lny+1

3B) y

3C) 1

3ln3ey+1

3D) 3lny+3

9) log5125

x–1

A) 3–1

2log5(x–1) B) 3log55–1

2log5(x–1)

C) log5125–log5x–1D) 3–log5x–1

Page45

10) logbxy7

z2

A) logbx+7logby–2logbz B) logbx+7logby+2logbz

C) logbx+logby7–logbz2D) logbx+logby7+logbz2

11) lnx

y

A) 1

2lnx–1

2lnyB)lnx–lny C) 1

2lnx

yD) 1

2lnx–lny

12) log 11

73

y2x

A) 1

7log 11 3–2log 11 y–log 11 xB)7log 11 3–2log 11 y–log 11 7

C) 1

7log 11 3–2log 11 y–2log 11 x D) log 11 3–log 11 y–log 11 x

13) log 5

3p4q

t2

A) 1

3log 5p+1

4log 5q–2 log 5tB)

1

3log 5p·1

4log 5q÷2 log 5t

C) 3

5log 5p+4

5log 5q–2

5log 5t D) 3 log 5p+4 log 5q–2 log 5t

14) logax43x+5

(x–2)2

A) 4logax+1

3loga(x+5)–2loga(x–2) B) 4logax–3loga(x+5)–2loga(x–2)

C) logax4+loga(x+5)–3–loga(x–2)2D) logax4+loga(x+5)1/3–loga(x–2)2

15)

log35x4y

9

A) 4

5log3x+1

5log3y–2

5B) 1

5(log3x4+log3y–2)

C) 1

5(log3x4y–log39) D) 4

5log3x–1

5log3y+2

5

Page46

16) log3x344–x

4(x+4)2

A) log3+3logx+1

4log(4–x)–log4–2log(x+4)

B) log3+logx3+log(4–x)1/4–log4–log(x+4)2

C) log(3x344–x)–log(4(x+4)2)

D) log3+3logx+1

4log(4–x)–log4+2log(x+4)

5 CondenseLogarithmicExpressions

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usepropertiesoflogarithmstocondensethelogarithmicexpression.Writetheexpressionasasinglelogarithmwhose

coefficientis1.Wherepossible,evaluatelogarithmicexpressions.

1) log cm+log cn

A) log c(mn) B) log cm·log cn C) log c(m +n) D) log c(m

n)

2) 3 log

b

m–log

b

n

A) log b

m3

nB) log bm3÷log bn C) log b(m3–n) D) log b(3m

n)

3) log 3(x+3)–log 3(x+6)

A) log 3

x+3

x+6B) log 3

x+3

x–6C) log 3–3 D) log 3(x2+9x+18)

4) 3 log x2+log x3

A) log x24 B) log x18 C) 3 log x6 D) log x2

5) log 248–log 23

A) 4 B) log 2144 C) log 245 D) log 248 1/3

6) 2lnx–1

4lny

A) lnx2

4y

B) lnx2

y4C) lnx24y D) lnx2y4

7) log10125+log108

A) 3 B) log101000 C) log10133 D) 3log1010

8) logx+log9

A) log9x B) (logx)(log9) C) logx

9D) log(x+9)

Page47

9) lnx+7lny

A) lnxy7B) lnx

y7C) ln7xy D) ln(x+7y)

10) 1

2log3x+log3y

A) log3yx B) log3

x

yC) log3xy D) log3

x

y

11) 9logby+6logbz

A) logby9z6B) 15logbyz C) logb(yz)15 D) 54logbyz

12) 9lna–7lnb

A) lna9

b7B) lna9

lnb7C) lna

b

16

D) ln9a

7b

13) 8ln(x–12)–9lnx

A) ln(x–12)8

x9B) lnx9(x–12)8C) ln8(x–12)

9x D) ln72x(x–12)

14) ( log am–log an)+4 log ak

A) log a

mk4

nB) log amk4n C) log a

m

k4nD) log a

4mk

n

15) 3 log 6x+5 log 6(x–6)

A) log 6x3(x–6)5B) log 6x(x–6)15 C) 15log 6x(x–6) D) log 6x(x–6)

16) 1

2(log5(r–5)–log5r)

A) log5r–5

rB) log5r–5

2r C) log5r–5

rD) log5r–5

r

17) 3log42+1

6log4(r–3)–1

2log4r

A) log486r–3

rB) log48r–3

12r C) log43r–9

12r D) log41

4

r–3

r

18) 1

3(log8x+log8y)

A) log83xy B) log83x+log83y

C) 3log8(xy) D) log83x+y

Page48

19) 1

4(log4x+log4y)–3log4(x+7)

A) log4

4xy

(x+7)3B) log4

4x+y

(x+7)3C) log4

4xy

3(x+7) D) log4

4x+4y

(x+7)3

20) 1

3[3ln(x+3)–lnx–ln(x2–3)]

A) ln3(x+3)3

x(x2–3) B) ln3(x+3)3(x2–3)

x

C) ln33(x+3)

x(x2–3) D) ln3x(x+3)3

(x2–3)

21) logx+log(x2–9)–log7–log(x–3)

A) logx(x+3)

7B) logx(x–9)

7(x–3) C) logx(x–9)(x–3)

7D) log2x+3)

10–x

6 UsetheChange–of–BaseProperty

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Usecommonlogarithmsornaturallogarithmsandacalculatortoevaluatetofourdecimalplaces

1) log 58

A) 1.2920 B) 0.7740 C) 1.6021 D) 0.2041

2) log 26 390

A) 1.8312 B) 0.5461 C) 4.0060 D) 1.1761

3) log 12 63.2

A) 1.6686 B) 0.5993 C) 2.8799 D) 0.7215

4) log 0.1 17

A) –1.2304 B) –0.8127 C) 0.2304 D) 2.2304

5) log π15

A) 2.3657 B) 0.4227 C) 1.6732 D) 0.6789

Solvetheproblem.

6) Usethemathematicalmodelforpowergain,G=logP0

Pi

10

,whereP0istheoutputpowerinwattsandPiis

theinputpowerinwatts.DeterminethepowergainG,indecibels,foranamplifierwithanoutputP0of19

wattsandaninputPiof1.9watts.Roundtofivedecimalplacesifnecessary.

A) 10dB B) 12.32996 dB C) 11 dB D) 15.57507 dB

Page49

4.4 ExponentialandLogarithmicEquations

1 UseLikeBasestoSolveExponentialEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheequationbyexpressingeachsideasapowerofthesamebaseandthenequatingexponents.

1) 4x=256

A) {4} B) {64} C) {5} D) {3}

2) 4(1+2x)=64

A) {1} B) {16} C) {4} D) {–1}

3) 2(5–3x)=1

16

A) {3} B) 1

8C) {8} D) {–3}

4) 2(3x+5)=1

16

A) {–3} B) 1

8C) {8} D) {3}

5) 3(3x–6)=27

A) {3} B) 1

9C) {9} D) {–3}

6) 729x=81

A) 2

3B) 3

2C) 4

5D) {4}

7) 9(x–3)

/

8=9

A) {7} B) {19} C) {11} D) 17

3

8) 125x=1

5

A) –1

6B) 1

6C) –1

3D) {–3}

9) 9x+1=27x–1

A) {5} B) {2} C) {4} D) {3}

10) ex+9=1

e5

A) {–14} B) {14} C) {4} D) {–4}

Page50

2 UseLogarithmstoSolveExponentialEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheexponentialequation.Expressthesolutionsetintermsofnaturallogarithms.

1) 7 9x=3.6

A) ln3.6

9ln7B) ln3.6

7ln9C) 9 ln3.6

ln7D) 3.6 ln9

ln7

2) 5 x+6=3

A) ln3

ln5–6 B) ln5

ln3+6 C) ln5

ln3+ln6 D) {ln3–ln5–ln6}

3) e2x=6

A) ln6

2B) ln2

6C) 3e D) {2ln6}

4) e x+7=5

A) {ln5–7} B) {e5+7} C) {e35} D) {ln12}

5) 4x+4=52x+5

A) 5ln5–4ln4

ln4–2ln5B) ln55

44–4

52C) {ln5–ln4} D) {7ln5–5ln4}

Solvetheexponentialequation.Useacalculatortoobtainadecimalapproximation,correcttotwodecimalplaces,forthe

solution.

6) 10x=3.91

A) 0.59 B) 8128.31 C) 1.36 D) 39.1

7) ex=4.5

A) 1.5 B) 0.65 C) 90.27 D) 12.24

8) 5x=18

A) 1.8 B) 4.65 C) 0.56 D) 0.88

9) 4ex=23

A) 1.75 B) 0.76 C) –1.75 D) –0.76

10) 25x=3.7

A) 0.38 B) 0.41 C) 9.44 D) 8.59

11) 3 x+8=4

A) –6.74 B) 8.79 C) 1.70 D) –0.78

12) e5x=8

A) 0.42 B) 0.20 C) 4.35 D) 10.40

13) e x+6=3

A) –4.90 B) –3.80 C) –4.75 D) 2.20

Page51

14) 7x=6x+7

A) 81.36 B) 3.36 C) 42.00 D) 40.68

15) e3x–10–10=1424

A) 5.76 B) 4.39 C) 2.42 D) 1.05

16) e2x+ex–6=0

A) 0.69 B) 0.69,1.10 C) 1.10,0.14 D) 0.14

3 UsetheDefinitionofaLogarithmtoSolveLogarithmicEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvethelogarithmicequation.Besuretorejectanyvaluethatisnotinthedomainoftheoriginallogarithmic

expressions.Givetheexactanswer.

1) log 2x=5

A) {32} B) {10} C) {25} D) {2.32}

2) log 5(x+3)=3

A) {122} B) {128} C) {240} D) {246}

3) log 6(x+3)=–3

A) –647

216 B) 649

216 C) –647

729 D) 649

729

4) log 3(x+2)+log 3(x–4)=3

A) {7} B) {7

,

–5} C) {–5} D) {8}

5) lnx=7

A) e7B) {ln7} C) 7eD) 7

ln1

6) 9ln(7x)=81

A) e9

7B) e 9

/

7C) e9D) 9

ln7

7) 2+6lnx=5

A) e 1

/

2B) e3

6C) ln1

2D) 3

6ln1

8) lnx+8=9

A) {e18–8} B) {e18+8} C) e9

2+8 D) {e9–8}

9) log910+log9x=1

A) { 9

10 }B){

10

9}C){

10 9}D){

1

10 }

10) log4(x2–3x)=1

A) {4

,

–1} B) {–4

,

1} C) {4} D) {1}

Page52

11) log2x+log2(x–3)=2

A) {4} B) {2} C) {1,–4} D) {–1,4}

12) log8(x+2)–log8x=2

A) { 2

63 } B) {8} C) { 1

32 }D){

63

2}

13) ln2+ln(x–1)=0

A) { 3

2}B){

2

3} C) {1} D) { 1

2}

14) log2(x+2)–log2(x–5)=3

A) {6} B) {1} C) {–6} D) ∅

15) log3(x+6)+log3(x–6)–log3x=2

A) {12} B) {12,–3} C) {–3} D) ∅

4 UsetheOne–to–OnePropertyofLogarithmstoSolveLogarithmicEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvethelogarithmicequation.Besuretorejectanyvaluethatisnotinthedomainoftheoriginallogarithmic

expressions.Givetheexactanswer.

1) log 3(x+5)=3+log 3(x+2)

A) –49

26 B) 3

26 C) 49

26 D) –3

26

2) log 15 (x+2)=1–log 15 x

A) {3} B) {–3} C) {5} D) {–5}

3) log3x=log4+log(x–1)

A) {4} B) 3

2C) {–4} D) –4

7

4) log(x+5)=log(5x–4)

A) 9

4B) 3

2C) –9

4D) 1

4

5) log(3+x)–log(x–5)=log3

A) {9} B) 5

2C) {–9} D) ∅

6) log 8(7x–1)=log 8(5x+4)

A) 5

2B) 3

2C) {3} D) ∅

7) log 8(4x+2)=log 8(4x+5)

A) {3} B) {0} C) 7

3D) ∅

Page53

8) log 6x2=log 6(4x+32)

A) {8

,

–4} B) {8} C) 4

3D) ∅

9) log4x=log5+log(x–3)

A) {15} B) 2

3C) {–15} D) –5

3

10) log(5+x)–log(x–3)=log5

A) {5} B) 3

2C) {–5} D) ∅

11) logx+log(x–1)=log30

A) {6} B) {–5} C) {6

,

–5} D) 31

2

12) lnx+ln(x+1)=ln56

A) {7} B) {8} C) {8

,

–7} D) 57

2

13) 2logx=log16

A) {4} B) {–4} C) {±4} D) 2

14) log(x+26)–log3=log(7x+1)

A) 23

20 B) 77

4C) –23

20 D) –77

4

15) 2logx–log6=log96

A) {24} B) {–24} C) {24

,

–24} D) 288

16) ln(x–6)+ln(x+1)=ln(x–15)

A) {–3} B) {3} C) {3,–3} D) ∅

17) ln(x–10)–ln(x+7)=ln(x–4)–ln(x+9)

A) –31

2B) 31

8C) 59

2D) ∅

5 SolveAppliedProblemsInvolvingExponentialandLogarithmicEquations

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) Findouthowlongittakesa$3000investmenttodoubleifitisinvestedat7% compoundedmonthly.Roundto

thenearesttenthofayear.UsetheformulaA=P1+r

n

nt.

A) 9.9years B) 10.1 years C) 9.7 years D) 10.3 years

2) TheformulaA=134e0.032tmodelsthepopulationofaparticularcity,inthousands,tyearsafter1998.When

willthepopulationofthecityreach168thousand?

A) 2005 B) 2006 C) 2007 D) 2008

Page54

3) Thefunctionf(x)=1+1.6ln(x+1)modelstheaveragenumberoffree–throwsabasketballplayercanmake

consecutivelyduringpracticeasafunctionoftime,wherexisthenumberofconsecutivedaysthebasketball

playerhaspracticedfortwohours.Afterhowmanydaysofpracticecanthebasketballplayermakeanaverage

of8consecutivefreethrows?

A) 78days B) 80days C) 276 days D) 278 days

4) ThepHofasolutionrangesfrom0to14.AnacidhasapHlessthan7.PurewaterisneutralandhasapHof7.

ThepHofasolutionisgivenbypH=–logxwherexrepresentstheconcentrationofthehydrogenionsinthe

solutioninmolesperliter.FindthehydrogenionconcentrationifthepH=14.

A) 10–14 B) 1014 C) 2.64 D) 0.07

5) ThepHofasolutionrangesfrom0to14.AnacidhasapHlessthan7.PurewaterisneutralandhasapHof7.

ThepHofasolutionisgivenbypH=–logxwherexrepresentstheconcentrationofthehydrogenionsinthe

solutioninmolesperliter.FindthehydrogenionconcentrationifthepH=5.4.

A) 3.98x10–6B) 3.98x10–5C) 2.51x10–5D) 2.51x10–6

6) Findouthowlongittakesa$2800investmenttoearn$400 interestifitisinvestedat9%compounded

quarterly.Roundtothenearesttenthofayear.UsetheformulaA=P1+r

n

nt.

A) 1.5years B) 1.7years C) 1.3 years D) 1.9 years

7) Cindywillrequire$19,000in2yearstoreturntocollegetogetanMBAdegree.Howmuchmoneyshouldshe

askherparentsfornowsothat,ifsheinvestsitat10%compoundedcontinuously,shewillhaveenoughfor

school?(Roundyouranswertothenearestdollar.)

A) $15,556 B) $15,702 C) $23,207 D) $12,736

8) Larryhas$2700toinvestandneeds$3100 in12 years.Whatannualrateofreturnwillheneedtogetinorderto

accomplishhisgoal,ifinterestiscompoundedcontinuously?(Roundyouranswertotwodecimals.)

A) 1.15% B) 1.48% C) 2.48% D) 3.48%

9) IfEmeryhas$1600toinvestat9%peryearcompoundedmonthly,howlongwillitbebeforehehas$2900?If

thecompoundingiscontinuous,howlongwillitbe?(Roundyouranswerstothreedecimalplaces.)

A) 6.633yrs,6.608yrs B) 0.575 yrs,0.551 yrs

C) 70.833yrs,6.83yrs D) 0.089 yrs,0.661 yrs

10) Thesizeofthecoyotepopulationatanationalparkincreasesattherateof4.8% peryear.Ifthesizeofthe

currentpopulationis194,findhowmanycoyotesthereshouldbein5years.Usey=yoe0.048tandroundto

thenearestwholenumber.

A) 247 B) 249 C) 245 D) 251

11) Thepopulationinaparticularcountryisgrowingattherateof1.8%peryear.If10,184,000peoplelivedtherein

1999,howmanywilltherebeintheyear2005?Usey=yoe0.018tandroundtothenearestten–thousand.

A) 11,350,000 B) 12,480,000 C) 11,120,000 D) 13,610,000

12) ThefunctionA=A0e–0.0077xmodelstheamountinpoundsofaparticularradioactivematerialstoredina

concretevault,wherexisthenumberofyearssincethematerialwasputintothevault.If500poundsofthe

materialareinitiallyputintothevault,howmanypoundswillbeleftafter120years?

A) 198pounds B) 297pounds C) 333 pounds D) 188 pounds

Page55

13) ThefunctionA=A0e–0.0099xmodelstheamountinpoundsofaparticularradioactivematerialstoredina

concretevault,wherexisthenumberofyearssincethematerialwasputintothevault.If500poundsofthe

materialareplacedinthevault,howmuchtimewillneedtopassforonly84poundstoremain?

A) 180years B) 185years C) 190 years D) 360 years

14) Thepopulationofaparticularcountrywas26 millionin1981;in1990

,

itwas31 million.Theexponential

growthfunctionA=26ektdescribesthepopulationofthiscountrytyearsafter1981.Usethefactthat9years

after1981thepopulationincreasedby5milliontofindktothreedecimalplaces.

A) 0.020 B) 0.179 C) 0.744 D) 0.030

15) Thepopulationofacertaincountryisgrowingatarateof2.5%peryear.Howlongwillittakeforthiscountryʹs

populationtodouble?Usetheformulat=ln2

k,whichgivesthetime,t,forapopulationwithgrowthratek,to

double.(Roundtothenearestwholeyear.)

A) 28years B) 29years C) 30 years D) 27years

4.5 ExponentialGrowthandDecay;ModelingData

1 ModelExponentialGrowthandDecay

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solve.

1) Thevalueofaparticularinvestmentfollowsapatternofexponentialgrowth.Intheyear2000,youinvested

moneyinamoneymarketaccount.Thevalueofyourinvestmenttyearsafter2000isgivenbytheexponential

growthmodelA=6900e0.049t.Howmuchdidyouinitiallyinvestintheaccount?

A) $6900.00 B) $7246.52 C) $338.10 D) $3450.00

2) Thevalueofaparticularinvestmentfollowsapatternofexponentialgrowth.Intheyear2000,youinvested

moneyinamoneymarketaccount.Thevalueofyourinvestmenttyearsafter2000isgivenbytheexponential

growthmodelA=2400e0.067t.Whenwilltheaccountbeworth$3355?

A) 2005 B) 2006 C) 2007 D) 2004

3) Thevalueofaparticularinvestmentfollowsapatternofexponentialgrowth.Intheyear2000,youinvested

moneyinamoneymarketaccount.Thevalueofyourinvestmenttyearsafter2000isgivenbytheexponential

growthmodelA=3500e0.067t.Bywhatpercentageistheaccountincreasingeachyear?

A) 6.7% B) 7.1% C) 7.3% D) 7.4%

4) ThefunctionA=A0e–0.00693xmodelstheamountinpoundsofaparticularradioactivematerialstoredina

concretevault,wherexisthenumberofyearssincethematerialwasputintothevault.If300poundsofthe

materialareinitiallyputintothevault,howmanypoundswillbeleftafter90years?

A) 161pounds B) 139pounds C) 135 pounds D) 167 pounds

5) ThefunctionA=A0e–0.00866xmodelstheamountinpoundsofaparticularradioactivematerialstoredina

concretevault,wherexisthenumberofyearssincethematerialwasputintothevault.If800poundsofthe

materialareplacedinthevault,howmuchtimewillneedtopassforonly218poundstoremain?

A) 150years B) 155years C) 160 years D) 300 years

6) Thepopulationofaparticularcountrywas22 millionin1982;in1992

,

itwas30 million.Theexponential

growthfunctionA=22ektdescribesthepopulationofthiscountrytyearsafter1982.Usethefactthat10years

after1982thepopulationincreasedby8milliontofindktothreedecimalplaces.

A) 0.031 B) 0.208 C) 0.649 D) 0.041

Page56

7) Thehalf–lifeofsilicon–32is710years.If50 gramsispresentnow,howmuchwillbepresentin300 years?

(Roundyouranswertothreedecimalplaces.)

A) 37.306 B) 48.557 C) 2.673 D) 0

8) Afossilizedleafcontains15%ofitsnormalamountofcarbon14.Howoldisthefossil(tothenearestyear)?Use

5600yearsasthehalf–lifeofcarbon14.

A) 15,299 B) 21,839 C) 1311 D) 35,828

9) Anendangeredspeciesoffishhasapopulationthatisdecreasingexponentially(A=A0ekt).Thepopulation5

yearsagowas1900.Today,only1100ofthefisharealive.Oncethepopulationdropsbelow100,thesituation

willbeirreversible.Whenwillthishappen,accordingtothemodel?(Roundtothenearestwholeyear.)

A) 22yearsfromtoday B) 23 yearsfromtoday

C) 21yearsfromtoday D) 24 yearsfromtoday

10) Thepopulationofacertaincountryisgrowingatarateof2.3%peryear.Howlongwillittakeforthiscountryʹs

populationtodouble?Usetheformulat=ln2

k,whichgivesthetime,t,forapopulationwithgrowthratek,to

double.(Roundtothenearestwholeyear.)

A) 30years B) 31years C) 32 years D) 29years

2 UseLogisticGrowthModels

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Solvetheproblem.

1) Thelogisticgrowthfunctionf(t)=360

1+5.0e–0.14t describesthepopulationofaspeciesofbutterfliestmonths

aftertheyareintroducedtoanon–threateninghabitat.Howmanybutterflieswereinitiallyintroducedtothe

habitat?

A) 60butterflies B) 360butterflies C) 5 butterflies D) 2butterflies

2) Thelogisticgrowthfunctionf(t)=720

1+8.0e–0.26t describesthepopulationofaspeciesofbutterfliestmonths

aftertheyareintroducedtoanon–threateninghabitat.Whatisthelimitingsizeofthebutterflypopulationthat

thehabitatwillsustain?

A) 720butterflies B) 80butterflies C) 8 butterflies D) 1440 butterflies

3) Thelogisticgrowthfunctionf(t)=360

1+5.0e–0.29t describesthepopulationofaspeciesofbutterfliestmonths

aftertheyareintroducedtoanon–threateninghabitat.Howmanybutterfliesareexpectedinthehabitatafter

20months?

A) 355butterflies B) 1200 butterflies C) 360 butterflies D) 7200 butterflies

4) Thelogisticgrowthfunctionf(t)=96,000

1+3199.0e–1.6t modelsthenumberofpeoplewhohavebecomeillwitha

particularinfectiontweeksafteritsinitialoutbreakinaparticularcommunity.Howmanypeoplebecameill

withthisinfectionwhentheepidemicbegan?

A) 30people B) 96,000 people C) 3199 people D) 3200 people

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5) Thelogisticgrowthfunctionf(t)=32,000

1+799e–1.2t modelsthenumberofpeoplewhohavebecomeillwitha

particularinfectiontweeksafteritsinitialoutbreakinaparticularcommunity.Howmanypeoplewereillafter

5weeks?

A) 10,736people B) 32,002 people C) 200 people D) 32,800 people

6) Thelogisticgrowthfunctionf(t)=94,000

1+3132.3e–1.3t modelsthenumberofpeoplewhohavebecomeillwitha

particularinfectiontweeksafteritsinitialoutbreakinaparticularcommunity.Whatisthelimitingsizeofthe

populationthatbecomesill?

A) 94,000people B) 188,000 people C) 3132 people D) 3133 people

3 ChooseanAppropriateModelforData

SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.

Presentdataintheformoftables.Forthedatasetshownbythetable,

a.Createascatterplotforthedata.

b.Usethescatterplottodeterminewhetheranexponentialfunctionoralogarithmicfunctionisthebest

choiceformodelingthedata.

1) NumberofHomesBuiltinaTownbyYear

Year NumberofHomes

1985 10

1991 92

1994 145

1997 192

2002 223

x

y

x

y

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2) PercentageofPopulationLivinginthe

SouthSuburbsofaLargeCity

Year Percent

1950 55

1960 69

1970 74

1980 75

2000 77

x

y

x

y

4 ExpressanExponentialModelinBasee

MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.

Rewritetheequationintermsofbasee.Expresstheanswerintermsofanaturallogarithm,andthenroundtothree

decimalplaces.

1) y=7(3)x

A) y=7exln3,y=7e1.099x B) y=3exln7,y=3e1.946x

C) y=7e3x,y=72.7181.099x D) y=(ln7)exln3,y=1.946e1.099x

2) y=41(2.3)x

A) y=41exln2.3,y=41e0.833x B) y=2.3exln41,y=2.3e3.714x

C) y=41e2.3x,y=412.7180.833x D) y=(ln41)exln2.3,y=3.714e0.833x

3) y=100(7.1)x

A) y=100exln7.1,y=100e1.960x B) y=7.1exln100,y=7.1e4.605x

C) y=100e7.1x,y=1002.7181.960x D) y=(ln100)exln7.1,y=4.605e1.960x

4) y=2.9(0.9)x

A) y=2.9exln0.9,y=2.9e–0.105x B) y=0.9exln2.9,y=0.9e1.065x

C) y=2.9e0.9x,y=2.92.718–0.105x D) y=(ln2.9)exln0.9,y=1.065e–0.105x

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Ch.4 ExponentialandLogarithmicFunctions

AnswerKey

4.1 ExponentialFunctions

1 EvaluateExponentialFunctions

2 GraphExponentialFunctions

26) A

3 EvaluateFunctionswithBasee

4 UseCompoundInterestFormulas

Page60

4.2 LogarithmicFunctions

1 ChangefromLogarithmictoExponentialForm

2 ChangeFromExponentialtoLogarithmicForm

3 EvaluateLogarithms

4 UseBasicLogarithmicProperties

5 GraphLogarithmicFunctions

6 FindtheDomainofaLogarithmicFunction

Page61

7 UseCommonLogarithms

8 UseNaturalLogarithms

4.3 PropertiesofLogarithms

1 UsetheProductRule

2 UsetheQuotientRule

3 UsethePowerRule

4 ExpandLogarithmicExpressions

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5 CondenseLogarithmicExpressions

6 UsetheChange–of–BaseProperty

4.4 ExponentialandLogarithmicEquations

1 UseLikeBasestoSolveExponentialEquations

2 UseLogarithmstoSolveExponentialEquations

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3 UsetheDefinitionofaLogarithmtoSolveLogarithmicEquations

4 UsetheOne–to–OnePropertyofLogarithmstoSolveLogarithmicEquations

5 SolveAppliedProblemsInvolvingExponentialandLogarithmicEquations

4.5 ExponentialGrowthandDecay;ModelingData

1 ModelExponentialGrowthandDecay

2 UseLogisticGrowthModels

6) A

3 ChooseanAppropriateModelforData

Page65

4 ExpressanExponentialModelinBasee

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