Deck 4: Exponential Functions

Question 1

The size , in thousands, of a certain animal population after years is given in the table below. By what percentage can the population be expected to grow over any 10-year period?

A) 51.63%
B) 50%
C) 62.89%
D) 64.33%

Answer 1

C

Question 2

Use exponential regression to determine what happens to when 1 is added to t.

A) 1.58 is added to
B) 3.87 is added to
C) is multiplied by 1.58
D) is multiplied by 3.87

Answer 2

C

Question 3

Find an exponential model for the following data set.

Answer 3

B

Question 4

The formula for an exponential function is , where is measured in months. Then the monthly percentage decay rate for is

A) 0.93%
B) 7.01%
C) 0.07%
D) 7%

Question 5

Solve the exponential equation

A)
B)
C)
D)

Question 6

The half-life of a certain radioactive substance is 6 years. What is the yearly percentage decay rate for this substance?

A) 8.54%
B) 10.91%
C) 11.18%
D) 8.33%

Question 7

The decay factor of an exponential function is 0.43. The initial value is 1.24. Then a formula for is

Question 8

Solve the equation

A)
B)
C)
D)

Question 9

Find an exponential model for the following data set.

Question 10

Find an exponential model for the following data set.

Question 11

Use exponential regression to determine what happens to when t is increased by 1 unit.

Question 12

If a function decreases by 5% each year, then the yearly decay factor is

A) 1.05
B) 5
C) 0.05
D) 0.95

Question 13

The monthly percentage decay rate for a certain exponential function is 6%. By what per- centage does the function decay in a week? (Assume there are four weeks in a month.)

A) 1.53%
B) 2.21%
C) 1.27%
D) 1.5%

Question 14

Find an exponential model for the following data set.

Question 15

A function shows constant percentage growth. Which of the following may be the graph of this function?

Question 16

Find an exponential model for the following data set.

Question 17

The size , in thousands, of a certain animal population after years is given in the table below. Use exponential regression to model the population size as a function of time.

Question 18

The formula for an exponential function is Then the decay factor is:

A) 643
B)
C)
D) 0.48

Question 19

A radioactive substance is decaying exponentially with yearly decay factor 0.95. What is the decade decay factor?

A) 0.1
B) 0.99
C) 9.5
D) 0.6

Question 20

Use exponential regression to determine what happens to when 1 is added to t.

A) is multiplied by 0.87.
B) is multiplied by 0.72.
C) 0.72 is added to .
D) 0.87 is added to

Question 21

A) 8.26
B) 8.92
C) 9.2
D) 9.09

Question 22

If a function decreases by 6% each year, then the yearly decay factor is

A) 1.06
B) 6
C) 0.06
D) 0.94

Question 23

Solve the equation

A)
B)
C)
D)

Question 24

The magnitude of an earthquake depends on the relative intensity of the quake. The relationship is Express the relative intensity as a function of the magnitude.

Question 25

Solve the exponential equation .

A)
B)
C)
D)

Question 26

The magnitude of earthquake 1 is 3.8, and the magnitude of earthquake 2 is 5.5. How do their intensities compare?

A) Earthquake 1 is 50.12 times as intense as earthquake 2.
B) Earthquake 1 is 1.7 times as intense as earthquake 2.
C) Earthquake 2 is 1.7 times as intense as earthquake 1.
D) Earthquake 2 is 50.12 times as intense as earthquake 1.

Question 27

Find an exponential model for the following data set.

Question 28

Find an exponential model for the following data set.

Question 29

The decay factor of an exponential function is 0.68. The initial value is 1.45. Then a formula for is

Question 30

A function shows constant percentage growth. Which of the following may be the graph of this function?

Question 31

The monthly percentage decay rate for a certain exponential function is 7%. By what per- centage does the function decay in a week? (Assume there are four weeks in a month.)

A) 1.8%
B) 2.76%
C) 1.14%
D) 1.75%

Question 32

The magnitude of earthquake 1 is 5.8. If earthquake 2 is 39.81 times as intense as earth- quake 1, find the magnitude of earthquake 2. Round your answer to 1 decimal place.

A) 7.4
B) 4.2
C) 45.6
D) 8.2

Question 33

The formula for an exponential function is Then the decay factor is:

A) 640
B)
C)
D) 0.96

Question 34

A) 7.72
B) 6.77
C) 7.8
D) 6.09

Question 35

Find an exponential model for the following data set.

Question 36

The formula for an exponential function is , where is measured in months. Then the monthly percentage decay rate for is

A) 0.93%
B) 7.01%
C) 0.07%
D) 7%

Question 37

Find an exponential model for the following data set.

Question 38

A radioactive substance is decaying exponentially with yearly decay factor 0.95. What is the decade decay factor?

A) 0.1
B) 0.99
C) 9.5
D) 0.6

Question 39

The half-life of a certain radioactive substance is 6 years. What is the yearly percentage decay rate for this substance?

A) 9.08%
B) 10.91%
C) 11.66%
D) 8.33%

Question 40

Find an exponential model for the following data set.

Question 41

The monthly percentage decay rate for a certain exponential function is 7%. By what per- centage does the function decay in a week? (Assume there are four weeks in a month.)

A) 1.8%
B) 2.43%
C) 0.79%
D) 1.75%

Question 42

The decay factor of an exponential function is 0.2. The initial value is 1.15. Then a formula for is

Question 43

A radioactive substance is decaying exponentially with yearly decay factor 0.95. What is the decade decay factor?

A) 0.1
B) 0.99
C) 9.5
D) 0.6

Question 44

If is 5.88, then the value of

A) 9.17
B) 7.51
C) 10.08
D) 7.44

Question 45

The size , in thousands, of a certain animal population after years is given in the table below. Use exponential regression to model the population size as a function of time.

Question 46

The magnitude of earthquake 1 is 3.6, and the magnitude of earthquake 2 is 6.9. How do their intensities compare?

A) Earthquake 1 is 1995.26 times as intense as earthquake 2.
B) Earthquake 1 is 3.3 times as intense as earthquake 2.
C) Earthquake 2 is 3.3 times as intense as earthquake 1.
D) Earthquake 2 is 1995.26 times as intense as earthquake 1.

Question 47

Solve the equation

A)
B)
C)
D)

Question 48

Use exponential regression to determine what happens to when t is increased by 1 unit.

Question 49

A function shows constant percentage growth. Which of the following may be the graph of this function?

Question 50

The formula for an exponential function is , where is measured in months. Then the monthly percentage decay rate for is

A) 0.94%
B) 6.01%
C) 0.06%
D) 6%

Question 51

The size , in thousands, of a certain animal population after years is given in the table below. By what percentage can the population be expected to grow over any 6-year period?

Question 52

If a function decreases by 7% each year, then the yearly decay factor is

A) 1.07
B) 7
C) 0.07
D) 0.93

Question 53

The formula for an exponential function is . Then the decay factor is:

A) 638
B)
C)
D) 0.57

Question 54

The magnitude of an earthquake depends on the relative intensity of the quake. The relationship is Express the relative intensity as a function of the magnitude.

Question 55

Solve the exponential equation

A)
B)
C)
D)

Question 56

The half-life of a certain radioactive substance is 8 years. What is the yearly percentage decay rate for this substance?

A) 6.51%
B) 8.3%
C) 9.22%
D) 6.25%

Question 57

Use exponential regression to determine what happens to when 1 is added to t.

Question 58

Use exponential regression to determine what happens to when 1 is added to t.

Question 59

If is 7.15, then the value of

A) 10.3
B) 8.59
C) 11.18
D) 9.16

Question 60

The magnitude of earthquake 1 is 5.9. If earthquake 2 is 13.49 times as intense as earth- quake 1, find the magnitude of earthquake 2. Round your answer to 1 decimal place.

A) 7
B) 4.8
C) 19.4
D) 8

Question 61

The size , in thousands, of a certain animal population after years is given in the table below. Use exponential regression to model the population size as a function of time.

Question 62

Find an exponential model for the following data set.

Question 63

Find an exponential model for the following data set.

Question 64

The size , in thousands, of a certain animal population after years is given in the table below. By what percentage can the population be expected to grow over any 6-year period?

Question 65

Use exponential regression to determine what happens to when t is increased by 1 unit.

Question 66

The magnitude of earthquake 1 is 4.6. If earthquake 2 is 12.59 times as intense as earth- quake 1, find the magnitude of earthquake 2. Round your answer to 1 decimal place.

A) 5.7
B) 3.5
C) 17.2
D) 6.1

Question 67

Solve the exponential equation

A)
B)
C)
D)

Question 68

Find an exponential model for the following data set.

Question 69

If is 2.1, then the value of

A) 6.76
B) 6.11
C) 7.53
D) 5.32

Question 70

Use exponential regression to determine what happens to when 1 is added to t.

Question 71

The decay factor of an exponential function is 0.61. The initial value is 1.48. Then a formula for is

Question 72

Find an exponential model for the following data set.

Question 73

If is 7.12, then the value of is

A) 18.8
B) 9.76
C) 19.26
D) 10.2

Question 74

A radioactive substance is decaying exponentially with yearly decay factor 0.93. What is the decade decay factor?

A) 0.09
B) 0.99
C) 9.3
D) 0.48

Question 75

The magnitude of earthquake 1 is 4.4, and the magnitude of earthquake 2 is 5.6. How do their intensities compare?

A) Earthquake 1 is 15.85 times as intense as earthquake 2.
B) Earthquake 1 is 1.2 times as intense as earthquake 2.
C) Earthquake 2 is 1.2 times as intense as earthquake 1.
D) Earthquake 2 is 15.85 times as intense as earthquake 1.

Question 76

The formula for an exponential function is Then the decay factor is:

A) 639
B)
C)
D) 0.62

Question 77

Use exponential regression to determine what happens to when 1 is added to t.

Question 78

Solve the equation

A)
B)
C)
D)

Question 79

The magnitude of an earthquake depends on the relative intensity of the quake. The relationship is Express the relative intensity as a function of the magnitude.

Question 80

Find an exponential model for the following data set.