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Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
The graph of an exponential function is given. Select the function for the graph from the functions listed.
1)
1)
A)
f(x) =4x
B)
f(x) = - 4-x
C)
f(x) = - 4x
D)
f(x) =4-x
2)
2)
A)
f(x) =3x+ 2
B)
f(x) =3x + 2
C)
f(x) =3x- 2
D)
f(x) =3x
3)
3)
A)
f(x) = - 4x
B)
f(x) =4-x
C)
f(x) = - 4-x
D)
f(x) =4x
4)
4)
A)
f(x) =2x
B)
f(x) = - 2-x
C)
f(x) = - 2x
D)
f(x) =2-x
5)
5)
A)
f(x) =4x- 1
B)
f(x) =4x - 1
C)
f(x) =4x
D)
f(x) =4x+ 1
6)
6)
A)
f(x) =2x+ 1
B)
f(x) =2x- 1
C)
f(x) =2x - 1
D)
f(x) =2x
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
For each 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, a logarithmic function, or a linear function is the
best choice for modeling the data.
7)
Percentage of Population Living in the South Suburbs of a Large City
Year Percent
1970 55
1980 70
1990 73
2000 75
2010 77
7)
Provide an appropriate response.
8)
A function f models the percentage of attendance at weekly welfare-to-work meetings as a
function of number of continuous weeks an employee stays at the same job. The graph of f
is shown in the figure.
a. Explain why f has an inverse that is a function.
b. Find f-1(20).
c. Describe in practical terms the meaning of f-1(20).
8)
For each 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, a logarithmic function, or a linear function is the
best choice for modeling the data.
9)
Number of Homes Built in a Town by Month
Year Number of Homes
1995 11
2001 91
2004 145
2007 191
2012 224
9)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
10)
Larry has $2500 to invest and needs $3000 in 16 years. What annual rate of return is required for
him to accomplish his goal, if interest is compounded continuously? (Round your answer to two
decimals.). Use the formula A = Pert.
10)
A)
1.35%
B)
2.35%
C)
3.35%
D)
1.14%
Use the compound interest formulas A = P 1 +r
n
nt and A = Pert to solve.
11)
Find the accumulated value of an investment of $6000 at 6% compounded continuously for 6 years.
11)
A)
$8160.00
B)
$8599.98
C)
$8511.11
D)
$8699.98
Find the domain of the logarithmic function. Write your answer in interval notation.
12)
f(x) =log7(x +8)
12)
A)
(-8, )
B)
(-, 0) (0, )
C)
(7, )
D)
(8, )
Simplify the expression.
13)
logzz
13)
A)
0
B)
z2
C)
1
D)
2z
Solve.
14)
The value of a particular investment follows a pattern of exponential growth. You invested money
in a money market account. The value of your investment t years after your initial investment is
given by the exponential growth model A =7500e0.062t. When will the account be worth $13,104?
14)
A)
10 years after the initial investment
B)
9 years after the initial investment
C)
8 years after the initial investment
D)
11 years after the initial investment
Find the composition.
15)
If f(x) =x2+4x and g(x) = x +2, find (f
g)(2).
15)
A)
0
B)
4 3
C)
14
D)
32
Solve the equation by expressing each side as a power of the same base and then equating exponents.
16)
4(3x - 5)=256
16)
A)
1
64
B)
128
C)
{-3}
D)
{3}
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.
17)
8logb y +7logb z
17)
A)
logb(yz)15
B)
logb(y8z7)
C)
56 logb(yz)
D)
15 logb(yz)
8
Simplify the expression.
18)
log4 1
18)
A)
1
4
B)
1
C)
4
D)
0
Find the composition.
19)
If f(x) =5x2- 6x and g(x) = - 3x, find (g
f)(x).
19)
A)
45x2- 6x
B)
5x2- 12
C)
-15x2+ 18x
D)
-15x3+ 18x2
Find the inverse of the one-to-one function.
20)
f(x) =(x + 4)3
20)
A)
f-1(x) =
3x- 64
B)
f-1(x) =x- 4
C)
f-1(x) =
3x+ 4
D)
f-1(x) =
3x- 4
9
Solve the problem.
21)
A research team collected data concerning a local welfare-to-work program. They found that the
more frequently a participant attended weekly group support meetings, the longer he or she would
keep the same job. The data are summarized in the graph below. Call the function f.
Find f-1(20).
21)
A)
32
B)
11
C)
45
D)
40
Use the graph of the function to draw the graph of the inverse function.
22)
22)
A)
B)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
23)
log7
4y
23)
A)
1
7log4 y
B)
4log7 y
C)
1
4log7 y
D)
1
4log7
4y
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places
24)
log6
24)
A)
1.2753
B)
1.5652
C)
0.6389
D)
0.2810
Find the domain of the logarithmic function. Write your answer in interval notation.
25)
f(x) = ln (8- x)
25)
A)
(-8, )
B)
(-, 8)
C)
(-, 8) (8, )
D)
(-, 0)
Find the inverse of the one-to-one function.
26)
f(x) =9
x
26)
A)
f-1(x) = - 9x
B)
f-1(x) =9x
C)
f-1(x) =9
x
D)
f-1(x) =x
9
Evaluate the expression without using a calculator.
27)
log327
27)
A)
3
B)
1
3
C)
1
D)
9
Use the compound interest formulas A = P 1 +r
n
nt and A = Pert to solve.
28)
Find the accumulated value of an investment of $19,000 at 5.5% compounded semiannually for 12
years.
28)
A)
$36,434.90
B)
$26,310.89
C)
$31,540.00
D)
$36,122.94
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.
29)
log x + log 14
29)
A)
log(14x)
B)
log x
14
C)
(log x)(log 14)
D)
log(x +14)
Solve the equation.
30)
ln(2x -5) - ln(9x) = ln 3
30)
A)
-1
5
B)
C)
-5
268
D)
-5
8998
Solve.
31)
Use the formula R = log a
T+ B to find the intensity R on the Richter scale, given that amplitude a is
248 micrometers, time T between waves is 3 seconds, and B is 2.3. Round answer to one decimal
place.
31)
A)
7.3
B)
6.7
C)
4.2
D)
1.9
Solve the exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms.
32)
e3x =6
32)
A)
ln 3
6
B)
{3 ln 6}
C)
2e
D)
ln 6
3
33)
e(x +8) =4
33)
A)
{e32}
B)
{ln 4-8}
C)
{e4+8}
D)
{ln 12}
13
Approximate the number using a calculator. Round the answer to three decimal places.
34)
23
34)
A)
3.322
B)
3.464
C)
4.000
D)
3.000
Find the inverse of the one-to-one function.
35)
f(x) =x11/12
35)
A)
f-1(x) =12
11 x
B)
f-1(x) =x12/11
C)
f-1(x) =x-12/11
D)
f-1(x) =x-11/12
Solve.
36)
The long jump record, in feet, at a particular school can be modeled by f(x) =20.7 +2.3 ln(x + 1)
where x is the number of years since the school was opened. What is the record for the long jump
16 years after the school opened? Round the answer to the nearest tenth.
36)
A)
26.9 ft
B)
23.0 ft
C)
27.2 ft
D)
27.1 ft
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
37)
logb
xy3
z8
37)
A)
logb x +logby3+logbz8
B)
logb x +3logb y -8logb z
C)
logb x +logby3-logbz8
D)
logb x +3logb y +8logb z
Determine whether the values in the table belong to an exponential function, a logarithmic function, a linear function, or
a quadratic function.
38)
x y
0 1
1 2
2 4
316
432
38)
A)
exponential
B)
linear
C)
quadratic
D)
logarithmic
Solve.
39)
The function A =A0e-0.01386x 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 900 pounds of the material are initially put into the vault, how many pounds will be left after 70
years?
39)
A)
321 lb
B)
341 lb
C)
630 lb
D)
549 lb
Solve the problem.
40)
Larry has $2900 to invest and needs $3400 in 13 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.)
40)
A)
3.44%
B)
2.44%
C)
1.22%
D)
1.44%
Solve the exponential equation by taking the logarithm on both sides. Express the solution set in terms of logarithms.
41)
83x =4.4
41)
A)
log 4.4
3 log 8
B)
4.4 log 3
log 8
C)
log 4.4
8 log 3
D)
3 log 4.4
log 8
Use the compound interest formulas A = P 1 +r
n
nt and A = Pert to solve.
42)
Find the accumulated value of an investment of $1200 at 6% compounded quarterly for 3 years.
42)
A)
$1254.81
B)
$1429.22
C)
$1434.74
D)
$1416.00
Find the composition.
43)
If f(x) =x2+ 10 and g(x) =x2+ 4, find (g
f)(3).
43)
A)
179
B)
35
C)
113
D)
365
Determine whether the values in the table belong to an exponential function, a logarithmic function, a linear function, or
a quadratic function.
44)
x y
1
5-1
1 0
5 1
25 2
125 3
44)
A)
exponential
B)
linear
C)
logarithmic
D)
quadratic
D)
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
45)
log10(1000x)
45)
A)
3+log10 x
B)
3log10 x
C)
30 +log10 x
D)
3x
Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.
46)
f(x) = x +1 and g(x) = x -1
46)
A)
not inverses
B)
inverses
Solve.
47)
The formula y = 1 +1.4 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 302 days of practice, what is the
average number of consecutive free throws the basketball player makes?
47)
A)
13 consecutive free throws
B)
9 consecutive free throws
C)
10 consecutive free throws
D)
12 consecutive free throws
Write the equation in its equivalent exponential form.
48)
2=logb4
48)
A)
4b=2
B)
2b=4
C)
42= b
D)
b2=4
Solve.
49)
The half-life of silicon-32 is 710 years. If 90 grams is present now, how much will be present in 600
years? Round the answer to three decimal places.
49)
A)
84.88 g
B)
0 g
C)
0.257 g
D)
50.102 g
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.
50)
9 log x +2 log y
50)
A)
log(xy)11
B)
18 log(xy)
C)
11 log(xy)
D)
log(x9y2)
17
Determine whether the values in the table belong to an exponential function, a logarithmic function, a linear function, or
a quadratic function.
51)
x y
025
1 5
2 0
3 5
425
51)
A)
exponential
B)
quadratic
C)
logarithmic
D)
linear
Find the domain of the logarithmic function. Write your answer in interval notation.
52)
f(x) = log(x - 9)
52)
A)
(-9, )
B)
(-, 0) (0, )
C)
(9, )
D)
(-, 9) (9, )
Solve.
53)
The first recorded population of a particular country was 23 million, and the population was
recorded as 34 million 6 years later. The exponential growth function A =23ekt describes the
population of this country t years since the first recording. Use the fact that 6 years later the
population increased by 11 million to find k to three decimal places.
53)
A)
0.075
B)
1.110
C)
0.065
D)
0.400
Evaluate the expression without using a calculator.
54)
ln e3.2
54)
A)
32
B)
3.2
C)
-3.2
D)
log 3.2
Graph the function by making a table of coordinates.
18
55)
f(x) =0.7x
55)
A)
B)
C)
D)
Evaluate the expression without using a calculator.
56)
log 105
56)
A)
10
B)
5
C)
log 5
D)
105
Solve the exponential equation by taking the logarithm on both sides. Use a calculator to obtain a decimal approximation,
correct to four decimal places, for the solution.
57)
38x =2.5
57)
A)
4.7320
B)
0.1043
C)
0.1469
D)
6.6724
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.
58)
log248 -log23
58)
A)
log2144
B)
log245
C)
log2481/3
D)
4
Solve.
59)
A city has been growing at a rate of 0.6% annually. If there are currently 4,711,000 residents in the
city, how many (to the nearest ten-thousand) would be living in this city seven years from now?
Use the function f(x) =4,711,000(2.7)0.006t.
59)
A)
4,940,000
B)
4,910,000
C)
12,720,000
D)
530,000
Find the domain of the logarithmic function. Write your answer in interval notation.
60)
f(x) =log2(x +7)2
60)
A)
(-, 0) (0, )
B)
(7, )
C)
(-, -7) (-7, )
D)
(-7, )
20
