Deck 5: Growth and Decay: An Introduction to Exponential Functions

Question 1

For the exponential function given, identify A) the initial value and B) the growth factor.

Answer 1

A. 19,000
B. 2. 7

Question 2

Write an equation in the form for an exponential function with initial value 46 and growth factor 1.9.

Answer 2

Question 3

Which equation in the form for an exponential function has initial value, 230,000, and growth factor, 1.2?

A)
B)
C)
D)

Answer 3

Question 4

Below are functions that give the population, P, in year, t, for four towns.
Choose the function for the town that has the largest initial population.

A)
B)
C)
D)

Question 5

Below are functions that give the population, P, in year, t, for four towns.
Choose the function for the town that has the smallest growth factor.

A)
B)
C)
D)

Question 6

Write a function in the form for an exponential function where and for every unit increase in x, the output is multiplied by 1.8.

Question 7

Choose the function of an exponential function where and for every unit increase in x, the output is multiplied by 2.1.

A)
B)
C)
D)

Question 8

Write a function in the form for an exponential function with an initial value of 50 whose output triples for each unit increase of the input.

Question 9

An outbreak of a flu virus begins with 6 people infected and the number of people infected increases by a factor of 4.2
each week. Find a formula that gives the number of people infected, I, as a function of the weeks, w, since the outbreak began.

Question 10

An outbreak of a flu virus begins with 4 people infected and the number of people infected increases by a factor of 2
each week.

A) Find a formula that gives the number of people infected, I, as a function of the weeks, w, since the outbreak began.
B) Use this formula to find the number of people infected after 10 weeks.

Question 11

When an event happens in a community, news travels fast. Assuming 4 people initially know the news and the number of people who hear the news increases by a factor of 4.3 each hour, find a formula that gives the number of people who hear the news, N, as a function of the hours, h, since the event happened.

Question 12

When an event happens in a community, news travels fast.

A) Assuming 2 people initially know the news and the number of people who hear the news increases by a factor of 2.8 each hour, find a formula that gives the number of people who hear the news, N, as a function of the hours, h, since the event happened.
B) Estimate how long, to the nearest hour, it will take for 120 people to hear the news.

Question 13

An investment is originally worth $19,000 and its worth increases by a factor of 1.008 each month. Find a formula that gives the investment's worth , W, as a function of the months, m, since the original investment.
Write your answer in form .

Question 14

An investment is originally worth $17,000 and its worth increases by a factor of 1.006 each month.

A) Find a formula that gives the investment's worth , W, as a function of the months, m, since the original investment.
B) Use the formula to find the worth of the investment after 16 months.Round your answer to the nearest cent.

Question 15

Match the function with its graph:

A)

B)

C)

D)

Question 16

The number of bacteria in a bacterial culture is 59,295 at the end of 5 hours. If the number of bacteria in the culture increases by a factor of 1.99 every hour, find the equation to describe the growth of the culture.
Write your answer in form. Round each portion of the answer to 2 decimal places if necessary.

Question 17

An institution promises that investments in their mutual funds will double every 8 years. If $5,000 is invested, how much will the investment be worth in 24 years?

Question 18

A quantity, Q, doubles every 5 years. Write a formula for the quantity of Q where T = the number of 5 year periods and the amount of the original substance is 580 grams.

Question 19

How many years does it take for this function to double?

Question 20

Determine whether the function represents exponential growth or decay.

A) Growth
B) Decay

Question 21

Determine whether the function represents exponential growth or decay.

A) Decay
B) Growth

Question 22

For the exponential function given, identify A) the initial value and B) the growth or decay factor.

Question 23

Write an equation in the form for an exponential function with initial value 3,700 and growth factor 1.9.

Question 24

Write a function in the form for an exponential function where and for every unit increase in x, the output is multiplied by 0.3.

Question 25

Write an equation for an exponential function (in the form ) that satisfies these two points:
and
Round values to 2 decimal places.

Question 26

Write a function in the form for an exponential function where and .

Question 27

Find the growth/decay factor (assuming exponential growth/decay) for a population that decreases from 29,000,000 to 24,940,000 in one year.

Question 28

Find the formula of the given exponential function.

Give your answer in form. Round values to 2 decimal places.

Question 29

A piece of equipment is originally worth $18,000 and its worth decreases by a factor of 0.6 each year.

A) Find a formula that gives the equipment's value , V, as a function of the years, y, since its purchase.
B) Use the formula to find the worth of the equipment after 3 years.Round your answer to the nearest cent.

Question 30

Find an exponential function where and Write your answer in form and round values to 2 decimal places.

Question 31

The half-life of Beryllium 11 is 13.81 seconds. If a sample initially contains 2,800 atoms, create a formula to represent the number of atoms, A, in the sample after T intervals of 13.81 seconds.

Question 32

The half-life of Flourine 20 is 11 seconds. If a sample initially contains 2,200 atoms, how long would it take for the sample to decay to 275 atoms?

Question 33

The half-life of Fluorine 18 is 1.82 hours. If a sample initially contains 6,400 atoms, how many atoms will be left after 3.64 hours? Round the answer to the nearest whole number if necesasry.

Question 34

The half-life of penicillin in a beef cow is approximately 30 hours. If a beef cow is administered 45 mL of penicillin, how long will it take for the animal to reach the acceptable level for butchering of 0.5 mL? (Round your answer to the nearest tenth of an hour.)

Question 35

The half-life of penicillin in a beef cow is approximately 30 hours. If the acceptable level for butchering of 0.5 mL, and the beef cow is administered 25 mL of penicillin, will it be at an acceptable level to butcher after 7 days?

Question 36

If the half-life of francium is 21 minutes, how long would it take for a 2,000 gram sample to decay to less than 60 grams? (Round the answer to the nearest minute.)

Question 37

If the half-life of francium is 21 minutes, how much of a 4,000 gram sample would be left after 20 minutes? (Round the answer to the nearest gram.)

Question 38

For an exponential function, where x is measured in months and and Find A) the 4-month growth factor and B) the monthly growth factor.
Round answers to 2 decimal places.

Question 39

For an exponential function, where x is measured in months and and , which of the following is the monthly growth factor of the function (Rounded to 2 decimal places.)?

A) 4.45
B) 1.16
C) 3.45
D) 0.22

Question 40

Suppose a town's population grows from 85,000 to 385,000 over 12 years.
Find A) the 12-year growth factor and B) the annual growth factor.
Round answers to 2 decimal places.

Question 41

Suppose a town's population grows from 25,000 to 290,000 over 6 years.
Choose the annual growth factor.
Round answers to 2 decimal places.

A) 265,000
B) 1.50
C) 44,166.67
D) 11.60

Question 42

Suppose an investment grows from 8,000 to 30,000 over 13 years.
Find A) the 13-year growth factor and B) the annual growth factor.
Round answers to 2 decimal places.

Question 43

Suppose an investment grows from 9,000 to 48,000 over 9 years.
Choose the annual growth factor.
Round answers to 2 decimal places.

A) 39,000
B) 5.33
C) 4,333.33
D) 1.20

Question 44

Determine whether the data is linear or exponential.

A) Exponential
B) Linear

Question 45

Determine which data is (roughly) exponSential.

A)

B)

C)

Question 46

Write an equation for a function that satisfies these two points:
and assuming that it is A) a linear function, in the form and B) an exponential function in the form .
Round values to 2 decimal places.

Question 47

Write a function in the form for an exponential function where and .

Question 48

Find the growth factor (assuming exponential growth) for a population that grows from 1,100,000 to 1,716,000 in one year.

Question 49

A new cell phone company has 600 subscribers their first year (year 0) and their business grows to 1,000 subscribers the next year (year 1).
Find a formula for the number of subscribers, C, as a function of the years in business, y, assuming…

A) linear growth (write your answer in the form ) , and
B) exponential growth (write your answer in the form )Now use these functions to predict how many subscribers they will have in their 20th year of business (year 19) assuming...
C) linear growth and
D) exponential growth.Round values to 2 decimal places.

Question 50

Find the equation of the given function.

Give your answer in or form.

Question 51

Find the equation of the given function.
?
Give your answer in or form. Round values to 2 decimal places.

Question 52

Choose the function that best matches the description:
When x is 0, y is 5.5, and when x increases 1 unit, y increases 1.42 units

A)
B)
C)
D)

Question 53

Choose the function that best matches the description:
When x is 0, y is 2, and when x increases 1 unit, y is multiplied by 1.74

A)
B)
C)
D)

Question 54

In an effort to control Johne's disease in dairy cattle, the state of Minnesota set a goal to reduce the number of cattle with the disease from 15,015 in 1990 to 1,629 in by the year 2000.

A) Assuming a linear model, what would the average rate of change be per year?
B) Assuming an exponential model, what would be the decay factor needed?
Round answers to 3 decimal places if necessary.

Question 55

Match the function with its graph:

A)

B)

C)

D)

Question 56

Match the function with its graph:

A)

B)

C)

D)

Question 57

Below are functions that give the population, P, in year, t, for four towns.
Choose the function for the town that has the largest initial population.

A)
B)
C)
D)

Question 58

Find the equation of the horizontal asymptote in the graph of

Question 59

Choose the function that best fits the graph.

A)
B)
C)
D)

Question 60

For the exponential function given find the y-intercept.
Write your answer as an ordered pair (x,y).

Question 61

Choose the graph that best fits the description of an exponential function, with C= and a=

A)

B)

C)

D)

Question 62

Compared to the function whose graph is given as a solid curve, what can you definitely say about the exponential function whose graph is dashed?

A) C is larger
B) C is smaller
C) a is larger
D) a is smaller

Question 63

Given the functions:
F(x) = 9 (11.9)^x
G(x) = 55 + 0.85x
H(x) = 92 (0.96)^x
K(x) = 35.7 - 4.7x
As , which function(s) approach ? Select all that apply.

A) f(x)
B) g(x)
C) h(x)
D) k(x)

Question 64

Given the functions:
F(x) = 97 (6.9)^x
G(x) = 57 + 0.81x
H(x) = 78 (0.94)^x
K(x) = 26.7 - 4.9x
As , which function(s) approach 0? Select all that apply.

A) f(x)
B) g(x)
C) h(x)
D) k(x)

Question 65

Given the functions:
F(x) = 119 (1.5)^x
G(x) = 69 + 0.41x
H(x) = 82 (0.89)^x
K(x) = 13.7 - 4.5x
As , which function(s) approach ? Select all that apply.

A) f(x)
B) g(x)
C) h(x)
D) k(x)

Question 66

Given the functions:
F(x) = 94 (9.7)^x
G(x) = 4 + 0.19x
H(x) = 73 (0.91)^x
K(x) = 40.3 - 9.5x
As , which function(s) approach ? Select all that apply.

A) f(x)
B) g(x)
C) h(x)
D) k(x)

Question 67

Given the functions:
F(x) = 114 (3.1)^x
G(x) = 20 + 0.79x
H(x) = 84 (0.91)^x
K(x) = 10.3 - 10.7x
As , which function(s) approach 0? Select all that apply.

A) f(x)
B) g(x)
C) h(x)
D) k(x)

Question 68

Given the functions:
F(x) = 45 (4.9)^x
G(x) = 10 + 0.81x
H(x) = 75 (0.91)^x
K(x) = 28.3 - 5.5x
As , which function(s) approach ? Select all that apply.

A) f(x)
B) g(x)
C) h(x)
D) k(x)

Question 69

Consider:
F(x) = 49.5 + 2.4x
G(x) = 22.6 (2)^x
Compare f(0) to g(0).

A) f(0) = g(0)
B) f(0) < g(0)
C) f(0) > g(0)
D) Unable to determine.

Question 70

Consider:
F(x) = 59.4 + 6.2x
G(x) = 55.7 (4.5)^x
Compare f(x) to g(x) as .

A) f(x) = g(x)
B) f(x) < g(x)
C) f(x) > g(x)
D) Unable to determine.

Question 71

Consider:
F(x) = 28.8 - 0.22x
G(x) = 28.8 (0.22)^x
Compare f(0) to g(0).

A) f(0) = g(0)
B) f(0) < g(0)
C) f(0) > g(0)
D) Unable to determine.

Question 72

Consider:
F(x) = 93.8 - 0.77x
G(x) = 93.8 (0.77)^x
Compare f(x) to g(x) as .

A) f(x) = g(x)
B) f(x) < g(x)
C) f(x) > g(x)
D) Unable to determine.

Question 73

A city has a growth factor of 1.16 every 7 years. If the population is currently 80,726, construct a function to describe the city's population each year. Round each part of the answer to 3 decimal places if necessary.

Question 74

A city has a decay factor of 0.89 every 8 years. If the population is currently 80,973, construct a function to describe the city's population each year. Round each part of the answer to 3 decimal places if necessary.

Question 75

Given the functions: Which functions have the same y-intercept? Select all that apply.

A) f(x) and g(x)
B) f(x) and h(x)
C) f(x) and k(x)
D) g(x) and h(x)
E) g(x) and k(x)
F) h(x) and k(x)

Question 76

Given the functions: Which functions are mirror images of each other across the y-axis? Select all that apply.

A) f(x) and g(x)
B) f(x) and h(x)
C) f(x) and k(x)
D) g(x) and h(x)
E) g(x) and k(x)
F) h(x) and k(x)

Question 77

Given the functions: Which functions are mirror images of each other across the x-axis? Select all that apply.

A) f(x) and g(x)
B) f(x) and h(x)
C) f(x) and k(x)
D) g(x) and h(x)
E) g(x) and k(x)
F) h(x) and k(x)

Question 78

For the exponential function given, identify A) the initial value and B) the growth (or decay) rate.
Enter the growth (or decay) rate as a positive number in percentage form.

Question 79

Find an exponential function with initial value 3.9 and growth rate 1.2.
Write your answer in form.

Question 80

Find an exponential function with initial value 30 and decay rate 0.1. Write your answer in form.

A)
B)
C)
D)