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– 2
B)
f(x) =4x+ 2
C)
f(x) =4x – 2
D)
f(x) =4x
2)
2)
A)
f(x) =5–x
B)
f(x) = – 5x
C)
f(x) =5x
D)
f(x) = – 5–x
3)
3)
A)
f(x) =5x
B)
f(x) =5x – 1
C)
f(x) =5x+ 1
D)
f(x) =5x– 1
4)
4)
A)
f(x) =5x – 2
B)
f(x) =5x+ 2
C)
f(x) =5x
D)
f(x) =5x– 2
5)
5)
A)
f(x) =5x
B)
f(x) = – 5–x
C)
f(x) = – 5x
D)
f(x) =5–x
6)
6)
A)
f(x) = – 3x
B)
f(x) =3–x
C)
f(x) =3x
D)
f(x) = – 3–x
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)
7)
Number of Homes Built in a Town by Month
Year Number of Homes
1995 11
2001 92
2004 146
2007 191
2012 224
8)
8)
Percentage of Population Living in the South Suburbs of a Large City
Year Percent
1970 55
1980 70
1990 74
2000 76
2010 77
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Solve the logarithmic equation. Give an exact answer.
9)
log30(x2– x) = 1
9)
A)
{5, 6}
B)
{–5, 6}
C)
{–5, –6}
D)
{1, 30}
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.
10)
3(x +7) =7
10)
A)
1.4097
B)
–5.2288
C)
7.5646
D)
–0.4771
Graph the function by making a table of coordinates.
11)
f(x) =1
2
x
11)
A)
B)
6
C)
D)
Solve the problem.
12)
The formula A =296e0.045t models the population of a particular city, in thousands, t years after
2011. When will the population of the city reach 444 thousand?
12)
A)
2021
B)
2020
C)
2022
D)
2019
Write the equation in its equivalent logarithmic form.
13)
8x=359
13)
A)
log8x =359
B)
log359x =8
C)
log3598= x
D)
log8359 = x
Use the compound interest formulas A = P 1 +r
n
nt and A = Pert to solve.
14)
14)
Find the accumulated value of an investment of $1800 at 8% compounded quarterly for 2 years.
A)
$1872.72
B)
$2108.99
C)
$2099.52
D)
$2088.00
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
15)
log x
100
15)
A)
–20x
B)
log x +2
C)
100x
D)
log x –2
Solve the logarithmic equation. Give an exact answer.
16)
16)
log6(x + 2) –log6 x = 2
A)
2
35
B)
1
18
C)
{6}
D)
35
2
Solve.
17)
17)
The rabbit population in a forest area grows at the rate of 8% monthly. If there are 260 rabbits in
September, find how many rabbits (rounded to the nearest whole number) should be expected
by next September. Use the function f(x) =260(2.7)0.08t.
A)
675 rabbits
B)
662 rabbits
C)
688 rabbits
D)
674 rabbits
Graph the function.
8
18)
Use the graph of f(x) =3x to obtain the graph of g(x) =3x + 3 + 1.
18)
A)
B)
C)
D)
Solve.
19)
19)
The long jump record, in feet, at a particular school can be modeled by f(x) =18.8 +2.2 ln(x + 1)
where x is the number of years since the school was opened. What is the record for the long jump
25 years after the school opened? Round the answer to the nearest tenth.
A)
26.0 ft
B)
25.8 ft
C)
25.9 ft
D)
21.0 ft
20)
20)
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 =8100e0.066t. By what percentage is the
account increasing each year?
A)
6.6%
B)
0.66%
C)
7.3%
D)
8.1%
Graph the function.
21)
21)
f(x) =log1/6x
A)
B)
10
C)
D)
Solve the logarithmic equation. Give an exact answer.
22)
log6(x2– 5x) = 1
22)
A)
{6, –1}
B)
{–6, 1}
C)
{1}
D)
{6}
23)
23)
log5 x +log5(x –24) = 2
A)
{–25}
B)
{–5}
C)
{25}
D)
{5}
Graph the function by making a table of coordinates.
11
24)
f(x) =0.9x
24)
A)
B)
C)
D)
Solve.
25)
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 800 pounds of the material are placed in the vault, how much time will need to pass for
only 171 pounds to remain?
25)
A)
400 yr
B)
200 yr
C)
205 yr
D)
210 yr
Use the compound interest formulas A = P 1 +r
n
nt and A = Pert to solve.
26)
26)
Find the accumulated value of an investment of $5000 at 7% compounded continuously for 6
years.
A)
$7709.81
B)
$7609.81
C)
$7503.65
D)
$7100.00
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
27)
logb
xy5
z4
27)
A)
logb x +5logb y +4logb z
B)
logb x +logby5–logbz4
C)
logb x +logby5+logbz4
D)
logb x +5logb y –4logb z
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.
28)
28)
log515 –log53
A)
1
B)
log5151/3
C)
log512
D)
log545
Solve the equation by expressing each side as a power of the same base and then equating exponents.
29)
3(3x – 6)=27
29)
A)
1
9
B)
{3}
C)
{–3}
D)
9
Determine whether the values in the table belong to an exponential function, a logarithmic function, a linear function,
or a quadratic function.
30)
30)
x y
0 4
1 2
2 0
3–2
4–4
A)
exponential
B)
quadratic
C)
logarithmic
D)
linear
Evaluate the expression without using a calculator.
31)
31)
log 0.01
A)
–1
2
B)
–2
C)
1
2
D)
2
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
32)
logb(yz8)
32)
A)
logb y +8logb z
B)
8logb y +8logb z
C)
logb y +logb(8z)
D)
8logb(yz)
Solve the logarithmic equation. Give an exact answer.
33)
33)
log2(x – 4) =3
A)
{12}
B)
{2}
C)
{10}
D)
{4}
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
34)
ln x
y
34)
A)
1
2 ln x – ln y
B)
ln x– ln y
C)
1
2 ln x –1
2 ln y
D)
1
2 ln x
y
Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm.
35)
y =4.3(0.5)x
35)
A)
y =0.5 ln e4.3x
B)
y =0.5e(ln 4.3)x
C)
y =4.3e(ln 0.5)x
D)
y =4.3 ln e0.5x
Evaluate the expression without using a calculator.
36)
log 103
36)
A)
log 3
B)
3
C)
103
D)
10
Solve the problem.
37)
37)
Find out how long it takes a $2800 investment to earn $500 interest if it is invested at 9%
compounded quarterly. Round to the nearest tenth of a year. Use the formula A = P 1 +r
n
nt.
A)
2 yr
B)
1.6 yr
C)
2.2 yr
D)
1.8 yr
Solve the logarithmic equation. Give an exact answer.
38)
38)
ln 2+ ln x = 0
A)
{2}
B)
C)
{ 2}
D)
1
2
Solve.
39)
An endangered species of fish has a population that is decreasing exponentially (A =A0ekt). The
population 5 years ago was 1600. Today, only 1000 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 year.
39)
A)
25 yr
B)
26 yr
C)
23 yr
D)
24 yr
40)
40)
The half–life of silicon–32 is 710 years. If 100 grams is present now, how much will be present in
800 years? Round the answer to three decimal places.
A)
0.041 g
B)
0 g
C)
92.487 g
D)
45.794 g
Provide an appropriate response.
41)
Graph f(x) =2xand g(x) =2x +3 in the same rectangular coordinate system.
41)
A)
B)
17
C)
D)
Solve.
42)
Use the formula R = log a
T+ B to find the intensity R on the Richter scale, given that amplitude a
is 304 micrometers, time T between waves is 3.8 seconds, and B is 3.1. Round answer to one
decimal place.
42)
A)
5
B)
1.9
C)
7.4
D)
7.5
Use the compound interest formulas A = P 1 +r
n
nt and A = Pert to solve.
43)
43)
Find the accumulated value of an investment of $17,000 at 6.5% compounded semiannually for 6
years.
A)
$20,596.30
B)
$24,805.42
C)
$23,630.00
D)
$24,953.40
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
44)
44)
log8(8x)
A)
x
B)
1
C)
8
D)
1 +log8 x
Evaluate the expression without using a calculator.
45)
45)
log1010,000
A)
4
B)
1
10000
C)
40
D)
–4
Simplify the expression.
46)
46)
log6 1
A)
1
6
B)
0
C)
6
D)
1
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
47)
47)
log2(7 ·3)
A)
log27–log23
B)
(log27)(log23)
C)
log27+log23
D)
log221
Provide an appropriate response.
48)
48)
Use a calculator to evaluate log729 to four decimal places.
A)
0.5779
B)
2.3075
C)
0.6173
D)
1.7304
Solve the problem.
49)
The function A =100e0.037t models the population of a particular city, in thousands, t years after
2011. When will the population of the city reach 130 thousand? Is the population increasing or
decreasing? Explain.
49)
A)
2020; Decreasing; The growth rate, –0.037, is negative
B)
2017; Decreasing; The growth rate, –0.037, is negative
C)
2019; Increasing; The growth rate, 0.037, is positive.
D)
2018; Increasing; The growth rate, 0.037, is positive.
Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
50)
ln y–z
50)
A)
y ln z
B)
–y ln z
C)
z ln y
D)
–z ln y
Graph the function.
51)
Use the graph of f(x) =4x to obtain the graph of g(x) =4x – 3.
51)