Free Printable Understanding Exponential Functions

1.

Which does y= 2(.5)^xrepresent?

a)

Exponential Growth

b)

Exponential Decay

2.

Which does y=.5(2)^x represent?

a)

Exponential Growth

b)

Exponential Decay

3.

What is the decay factor of the situation represented by f(x)=10(0.3)^x?

a)

.7

b)

0.3

c)

.3 %

d)

70%

4.

This is the horizontal line which the values of the function y = a*b^xcannot fall below :

a)

Asymptote; x=0

b)

Growth Factor

c)

Axis of symmetry

d)

Asymptote; y=0

5.

If a table's pattern is that the f(x) values are being divided by 3, what is the common ratio?

a)

3

b)

-3

c)

1/3

d)

-1/3

6.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

7.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

8.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

9.

What is the common ratio for the sequence:

28, 14, 7, 3.5... (Hint: What is the multiplier?)

a)

2

b)

1/2

c)

-14

d)

-7

10.

What is the common ratio for the sequence:

3, 15, 75... ((Hint: What is the multiplier?))

a)

12

b)

1/5

c)

5

11.

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

a)

(.27)^x

b)

.27

c)

13

d)

3.51

12.

Is the pictured graph growth, decay, or linear or none?

a)

Growth

b)

Decay

c)

Linear

d)

Quadratic

13.

Is the pictured graph growth, decay, or linear or none?

a)

Growth

b)

Decay

c)

Linear

d)

Quadratic

14.

What is the range of f(x) = 5^x?

a)

-∞ ≤ x ≤ ∞

b)

-∞ ≤ y ≤ ∞

c)

x > 0

d)

y > 0

15.

What does the y-intercept of the graph represent?

a)

The amount of grams the material is gaining.

b)

The amount of grams the material is losing.

c)

The amount of grams remaining after so many years.

d)

The initial amount of grams.

16.

Which of the following is an increasing exponential function whose y-intercept is 50?

a)

y = 50(.05)^x

b)

y = 50x - 4

c)

y = (2)^x + 50

d)

y = 50(1.4)^x

17.

The amount of ants in a colony, f, that is decaying can be modeled by f(x) = 800(.87)^x, where x is the number of days since the decay started. By what percentage is the colony decaying?

a)

87%

b)

13%

c)

800%

d)

8.7%

18.

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

a)

$0.29

b)

$2,900,000,000

c)

$46,704.79

d)

$145,000

19.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

a)

The predicted increase in number of elephants in the refuge each year.

b)

The predicted decrease in number of elephants in the refuge each year.

c)

The number of years it will take for the elephant population to stop increasing.

d)

The initial amount of elephants in the park.

20.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

a)

Increasing

b)

Decreasing

21.

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?

a)

The number of elephants was 1,015 in 1975.

b)

The number of elephants increases by 1.5% each year.

c)

The number of elephants increases by 101.5% each year.

d)

The number of elephants is multiplied by 1.015 each year.

22.

The amount of ibuprofen (medicine for headaches) breaks down by 30% each hour. If a person took a 200 milligram ibuprofen, how much will be left after 3 hours?

a)

5.4 mg

b)

68.6 mg

c)

.0054 mg

d)

2,400,000 mg

23.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

a)

y=8(15,000)^x

b)

y=15,000(1 + .08)^x

c)

y=15,000(1 - .08)^x

d)

y=15,000(0.08)^x

24.

Which function represents the table of values?

a)

f(x) = 4x

b)

f(x) = x³

c)

f(x) = 4^x

d)

f(x) = 4^x-1

25.

Find the exponential model of the function.

a)

y = 100(8.8)^x

b)

y = 100(1.88)^x

c)

y = 100(.88)^x

d)

y = 100(.12)^x

26.

A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 6 weeks and obtains the following data: How much is left after 12 weeks?

a)

15

b)

21

c)

17

d)

19

27.

Barbers Hill host a single-elimination baseball tournament that begins with 64 teams. After the 1st round, 32 teams remain. After the 2nd round, 16 teams remain. And so forth...What equation represents this scenario?

a)

y = 64(2)^x ; exponential growth

b)

y = 64(1/2)^x ; exponential decay

c)

y = 64 - 2x ; linear

d)

y = 64x² ; quadratic

28.

Barbers Hill host a single-elimination baseball tournament that begins with 64 teams. After the 1st round, 32 teams remain. After the 2nd round, 16 teams remain. And so forth...Which table represents the scenario?

a)

b)

c)

d)

29.

Barbers Hill host a single-elimination baseball tournament that begins with 64 teams. After the 1st round, 32 teams remain. After the 2nd round, 16 teams remain. And so forth...What is the reasonable domain?

a)

x ≥ 0

b)

0 < y ≤ 64

c)

0, 1, 2, 3, 4, 5, 6

d)

1, 2, 4, 8, 16, 32, 64

30.

Barbers Hill host a single-elimination baseball tournament that begins with 64 teams. After the 1st round, 32 teams remain. After the 2nd round, 16 teams remain. And so forth...What is the reasonable range?

a)

x ≥ 0

b)

0 < y ≤ 64

c)

0, 1, 2, 3, 4, 5, 6

d)

1, 2, 4, 8, 16, 32, 64

31.

Barbers Hill host a single-elimination baseball tournament that begins with 64 teams. After the 1st round, 32 teams remain. After the 2nd round, 16 teams remain. And so forth...After how many rounds will 4 teams remain in the tournament?

a)

7

b)

4

c)

3

d)

5

32.

Barbers Hill host a single-elimination baseball tournament that begins with 64 teams. After the 1st round, 32 teams remain. After the 2nd round, 16 teams remain. And so forth...What is the decay factor in this scenario?

a)

2

b)

32

c)

1/4

d)

1/2

Understanding Exponential Functions

Total questions: 32

Worksheet time: 44mins

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