Deck 8: Exponential and Logarithmic Functions and Applications

Question 1

Answer 1

B

Question 2

Approximate the function value from the graph.

A) 2
B) 1
C) 0
D) -1

Answer 2

D

Question 3

Answer 3

D

Question 4

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

Question 5

Question 6

Question 7

Which of the following specifies a one-to-one function?

A) h = {(1,1), (2,2), (3,1)}
B) f = {(0,1), (0,2), (1,3)}
C) g = {(1,1), (2,2), (3,2)}
D) None of the above are one-to-one functions.

Question 8

Approximate the function value from the graph.

A) 5
B) 0
C) 2
D) 1

Question 9

Determine if the function is one-to-one by using the horizontal line test.

A) No, because the line y = x intersects the curve at more than one point.
B) No, because the line y = -1 intersects the curve at more than one point.
C) No, because the line x = -1 intersects the curve at more than one point.
D) Yes

Question 10

Approximate the function value from the graph.

A) 2
B) 1
C) 0
D) 3

Question 11

The volume of a can that is 12 centimeters (cm) tall is approximated by the functionv ,
where r is the radius of the can in cm. Chicken soup costs $0.01 per milliliter (mL) and since , we can say that chicken soup costs . The cost to fill a 12 cm tall can
with chicken soup is given by C(v) = 0.01v, where v is the volume of the can in .
a. Find and interpret its meaning in the context of this problem.
b. Approximate to the nearest cent the cost to fill a 12 cm can with chicken soup if the can's radius
is 5 cm.

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Write the word or phrase that best completes each statement or answers the question.
The cost in dollars of producing x toy cars is C(x) = 1.8x + 2. The revenue for selling x toy cars is
R(x) = 6.08x. To calculate profit, subtract the cost from the revenue.
a. Write and simplify a function P that represents profit in terms of x.
b. Find the profit of producing 50 toy cars.

Question 18

Question 19

Question 20

Question 21

Write the word or phrase that best completes each statement or answers the question.
Write an equation of the inverse for the one-to-one function

Question 22

Question 23

Write an equation of the inverse for the one-to-one function as defined.

Question 24

Write the word or phrase that best completes each statement or answers the question.
Graph the function . Plot at least three points.

Question 25

Write an equation of the inverse for the one-to-one function

Question 26

Write the word or phrase that best completes each statement or answers the question.
Solve the equation.

Question 27

Question 28

Evaluate the expression by using a calculator. Round to 4 decimal places.

A) 451.0879
B) 0.0022
C) -21.9911
D) -451.0879

Question 29

Determine if the function is one-to-one by using the horizontal line test.

A) Not one-to-one
B) One-to-one

Question 30

Write an equation of the inverse for the one-to-one function f (x) = 2x - 9.

Question 31

Graph the function

Question 32

Graph the function

Question 33

Write the word or phrase that best completes each statement or answers the question.
Verify that f and g are inverse functions by showing that

Question 34

Write an equation of the inverse for the one-to-one function

Question 35

Write the word or phrase that best completes each statement or answers the question.
Verify that f and g are inverse functions by showing that

Question 36

Scientists often use a process called carbon dating to estimate the age of archaeological finds. The process measures the amount of carbon-14, a radioactive isotope with a half-life of 5,730 years. If a
Sample of wood from an ancient artifact had 12 grams of carbon-14 initially, the amount remaining, in
Grams, is given by where t is the number of years since the tree died. How many grams would be present after 5,730
Years?

A) 3 g
B) 24 g
C) 0.27 g
D) 6 g

Question 37

True/False: are inverse functions because

A) False
B) True

Question 38

Evaluate the expression by using a calculator. Round to 4 decimal places.

A) 9.0827
B) 8.0000
C) 14.2457
D) 11.0357

Question 39

Write the word or phrase that best completes each statement or answers the question.
Graph the function . Plot at least three points.

Question 40

Question 41

Write the equation in logarithmic form.

Question 42

Write the equation in exponential form.

Question 43

Evaluate without the use of a calculator.

Question 44

Evaluate without the use of a calculator.

Question 45

Which is a logarithmic function?

Question 46

In 2000, the population of Sheboygan, WI was about 113,000 and was growing at a rate of 0.85% per year. Use an exponential function to predict the population in 2021 to the nearest whole
Number.

A) 134,981
B) 128,481
C) 460,982,820
D) 145,034

Question 47

Evaluate without the use of a calculator.

Question 48

The population of bacteria culture was 2000 at noon, and was increasing at a rate of 10% per hour. The number can be found using the function where t is the number of hours past noon. Predict the population 9 hours later, at 9 PM to the nearest
Whole number.

A) 4716
B) 19,800
C) 2716
D) 6736

Question 49

Evaluate without the use of a calculator.

Question 50

Evaluate without the use of a calculator.

Question 51

In 2000, the population of Sheboygan, WI was about 113,000 and was growing at a rate of 0.85% per year. Find an exponential function that describes the population P in terms of t, the number of
Years after 2000.

Question 52

Write the word or phrase that best completes each statement or answers the question.
Scientists often use a process called carbon dating to estimate the age of archaeological finds. The
process measures the amount of carbon-14, a radioactive isotope with a half-life of 5730 years. If a
sample of wood from an ancient artifact had 13 grams of carbon-14 initially, the amount remaining, in
grams, is given by where t is the number of years since the tree died. How many grams would be present after 22,920
years?

Question 53

Write the equation in exponential form.

Question 54

Write the word or phrase that best completes each statement or answers the question.
Evaluate without the use of a calculator.

Question 55

Evaluate without the use of a calculator.

A) -2
B) 4
C) 12
D) 2

Question 56

Write the equation in exponential form.

Question 57

Write the word or phrase that best completes each statement or answers the question.
Evaluate without the use of a calculator.

Question 58

Evaluate without the use of a calculator.

Question 59

Write the equation in logarithmic form.

Question 60

Write the word or phrase that best completes each statement or answers the question.
Write the equation in exponential form.

Question 61

Graph y = f (x).

Question 62

Find the domain of the function and express the domain in interval notation.

Question 63

Write the word or phrase that best completes each statement or answers the question.
Graph y = f (x).

Question 64

Find the domain of the function and express the domain in interval notation.

Question 65

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers.

Question 66

Evaluate the expression.

Question 67

Write the word or phrase that best completes each statement or answers the question.
Find the domain of the function and express the domain in interval notation.

Question 68

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers.

Question 69

Write the word or phrase that best completes each statement or answers the question.
The level of a sound in decibels is calculated using the formula where I is the intensity of the sound waves in watts per square meter. The sound intensity inside a
typical car at 60 mph is 0.00001 watts per square meter. How many decibels is that?

Question 70

Use a calculator to approximate the logarithm. Round to 3 decimal places.

Question 71

The level of a sound in decibels is calculated using the formula where I is the intensity of the sound waves in watts per square meter. The softest sound that a human can hear has an intensity of 10-12 watts per square meter. How many decibels is that?

A) 10
B) 24
C) -12
D) 0

Question 72

Evaluate the expression.

A) 24
B) 143
C) 13
D) 11

Question 73

Find the domain of the function and express the domain in interval notation.

Question 74

Expand into a sum and/or difference of logarithms. Assume all variables represent positive real numbers.

Question 75

Compare the expressions by approximating their values on a calculator. Which two expressions are equivalent?

Question 76

Evaluate the expression.

Question 77

Use a calculator to approximate the logarithm. Round to 4 decimal places.

Question 78

Evaluate the expression.

Question 79

Use a calculator to approximate the logarithm. Round to 4 decimal places.

Question 80

The level of a sound in decibels is calculated using the formula where I is the intensity of the sound waves in watts per square meter. A jackhammer puts out 1 watt per square meter. How many decibels is that?

A) 12
B) 10
C) 120
D) 1200