Deck 12: Logarithmic and Exponential Functions

Question 1

Solve.
The number of books in a small library increases according to the function B = 7300e0.05t, where t is measured in years. How many books will the library have after 9 years?

A) 2532
B) 5829
C) 20,574
D) 11,449

Answer 1

D

Question 2

Solve.
Use the formula N = Iekt, where N is the number of items at time t, I is the initial amount, and k is a growth constant equal to the percent of growth (expressed in decimal form) per unit of time.
There are currently 70 million cars in a certain country, increasing by 3% annually. How many
Years will it take for this country to have 97 million cars? Round to the nearest year.

A) 110 yr
B) 4 yr
C) 9 yr
D) 11 yr

Answer 2

D

Question 3

Evaluate the given function.

Answer 3

B

Question 4

Solve.
Susan purchased a painting in the year 2000 for $3000. Assuming an exponential rate of inflation of 3.8% per year, how much will the painting be worth 7 years later?

A) $7812.90
B) $9176.03
C) $4891.02
D) $3914.21

Question 5

Evaluate the given function.

Question 6

Evaluate the given function.

Question 7

Compute the compound interest.
$5000 is invested at 9% compounded quarterly. In how many years will the account have grown to $10,500? Round to the nearest tenth of a year.

A) 8.3 yr
B) 8.6 yr
C) 1.1 yr
D) 12.1 yr

Question 8

Compute the compound interest.
How long must $4200 be in a bank at 6% compounded annually to become $7521.56? (Round to the nearest year.)

A) 10 yr
B) 11 yr
C) 12 yr
D) 9 yr

Question 9

Evaluate the given function.

Question 10

Evaluate the given function.

Question 11

Evaluate the given function.

Question 12

Solve.
The function

A) 900 lb
B) 168 lb
C) 178 lb
D) 588 lb

Question 13

Solve.
The function A = A0e-0.01155x 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 placed in the vault, how much time will need to pass for only 53
Pounds to remain?

A) 160 yr
B) 150 yr
C) 155 yr
D) 300 yr

Question 14

Evaluate the given function.

Question 15

Solve.
One method to determine the time since an animal died is to estimate the percentage of carbon-14 remaining in its bones. The percent P in decimal form of carbon-14 remaining x years is given by
P(x) = e-0.000121x. Approximate (to the nearest whole year) the age of a fossil if there is 65% of
Carbon-14 remaining.

A) 1546
B) -34,499
C) -15,469
D) 3560

Question 16

Compute the compound interest.
How long will it take for $5000 to grow to $15,500 at an interest rate of 3.1% if the interest is compounded quarterly? Round the number of years to the nearest hundredth.

A) 37.06 yr
B) 100.39 yr
C) 36.64 yr
D) 146.55 yr

Question 17

Compute the compound interest.
How long will it take for $8900 to grow to $12,400 at an interest rate of 3.5% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

A) 3.5 yr
B) 947.56 yr
C) 0.95 yr
D) 9.48 yr

Question 18

Evaluate the given function.

Question 19

Solve.
There are currently 51 million cars in a certain country, increasing exponentially by 4.4% annually. How many years will it take for this country to have 60 million cars? Round to the nearest year.

A) 3 yr
B) 4 yr
C) 2 yr
D) 50 yr

Question 20

Solve.
The population of a small country increases according to the function B = 1,600,000e0.04t, where t is measured in years. How many people will the country have after 2 years?

A) 1,923,623
B) 1,755,056
C) 4,041,166
D) 1,733,259

Question 21

Find all intercepts for the given function. Round to the nearest tenth if necessary.

Question 22

Find all intercepts for the given function. Round to the nearest tenth if necessary.

Question 23

Solve the problem.

Question 24

Solve the problem.

Question 25

Find all intercepts for the given function. Round to the nearest tenth if necessary.

Question 26

Find all intercepts for the given function. Round to the nearest tenth if necessary.

Question 27

Solve the problem.

Question 28

Solve the problem.

Question 29

Solve the problem.
Yearly sales of an electronic device S(t), in millions of dollars, t years after 1998 can be estimated by

A) About 1999
B) About 2001
C) About 2000
D) About 2002

Question 30

Solve the problem.

Question 31

Solve the problem.

Question 32

Solve the problem.

Question 33

Solve the problem.

Question 34

Solve the problem.
The population growth of an animal species is described by F(t) = 300 + 20 log3 (2t + 1), where t is measured in months. Find the population of this species in an area 4 month(s) after the species is
Introduced.

A) 260
B) 180
C) 340
D) 480

Question 35

Solve the problem.

Question 36

Solve the problem.

Question 37

Solve.
The half-life of silicon-32 is 710 years. If 100 grams is present now, how much will be present in 900 years? (Round your answer to three decimal places.)

A) 91.589 g
B) 0.015 gC)0g
D) 41.535 g

Question 38

Solve the problem.

Question 39

Solve.
The number of acres in a landfill is given by the function B = 2800e-0.05t, where t is measured in years. How many acres will the landfill have after 2 years? (Round to the nearest acre.)

A) 2534 acres
B) 2224 acres
C) 2800 acres
D) 6447 acres

Question 40

Solve the problem.

Question 41

Evaluate. Round to the nearest thousandth, if necessary.

Question 42

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 43

Evaluate the given function.

Question 44

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 45

Evaluate the given function.

Question 46

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 47

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 48

Evaluate. Round to the nearest thousandth, if necessary.

Question 49

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 50

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 51

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 52

Evaluate the given function.
f(x) = 12log3 (x - 3), f(12)

A) 2
B) 29.5796822
C) 6
D) 24

Question 53

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 54

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 55

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 56

Evaluate the given function.

Question 57

Evaluate the given function.

Question 58

Determine the equation of the horizontal asymptote for the graph of this function, and state the domain and range of
this function.

Question 59

Evaluate. Round to the nearest thousandth, if necessary.

Question 60

Evaluate. Round to the nearest thousandth, if necessary.

Question 61

Rewrite in logarithmic form.
The population growth of an animal species is described by F(t) = 600 + 60 log3 (2t + 1) where t is the number of months since the species was introduced. Find the population of this species in an
Area 40 month(s) after the species is introduced.

A) 840
B) 5460
C) 2750
D) 430

Question 62

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real
numbers.

Question 63

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real
numbers.

Question 64

Rewrite in logarithmic form.

Question 65

Evaluate. Round to the nearest thousandth, if necessary.

Question 66

Rewrite in logarithmic form.

Question 67

Evaluate. Round to the nearest thousandth, if necessary.

Question 68

Evaluate. Round to the nearest thousandth, if necessary.

Question 69

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real
numbers.

Question 70

Rewrite as a single logarithm using the product rule for logarithms. Assume all variables represent positive real
numbers.

Question 71

Evaluate. Round to the nearest thousandth, if necessary.

Question 72

Rewrite in logarithmic form.
The space in a landfill decreases with time as given by the function F(t) = 320 - 40 log5 (4t + 1), where t is measured in years. How much space is left when t = 31?

A) 200
B) 440
C) 240
D) 110

Question 73

Rewrite as the sum of two or more logarithms using the product rule for logarithms. Assume all variables represent
positive real numbers.

Question 74

Rewrite in logarithmic form.

Question 75

Evaluate. Round to the nearest thousandth, if necessary.

Question 76

Rewrite in logarithmic form.
The number of visitors to a tourist attraction (for the first few years after its opening) can be approximated by

A) 58 visitors
B) 130 visitors
C) 80 visitors
D) 53 visitors

Question 77

Rewrite in logarithmic form.

Question 78

Evaluate. Round to the nearest thousandth, if necessary.

Question 79

Rewrite in logarithmic form.

Question 80

Rewrite in logarithmic form.
The sales of a new product (in items per month) can be approximated by

A) 500 items per month
B) 2300 items per month
C) 1300 items per month
D) 400 items per month