Free Printable Test 9: Exponential Functions REVIEW

1.

Which of the following is an exponential function?

a)

y = x²

b)

f(x) = 3x³

c)

y = x³

d)

f(x) = 3^x

2.

What is the initial value in y=4(2)^x

a)

4

b)

2

c)

x

3.

What is the y-intercept in y=4(2)^x

a)

(4,0)

b)

(0,2)

c)

x

d)

(0,4)

e)

(4,2)

4.

What is the starting amount in the problem below?

f(t) = 300(1.05)^t

a)

300

b)

1.05

c)

t

d)

y

5.

What is the growth rate in the problem below?

f(t) = 300(1.05)^t

a)

300

b)

1.05

c)

t

d)

y

6.

b⁰=

a)

-1

b)

0

c)

1

7.

The y-intercept for any function in the form

y=b^x

a)

(0,0)

b)

(0,1)

c)

(1,0)

8.

Describe this function.

a)

Exponential Growth

b)

Exponential Decay

c)

Linear Positive

9.

a)

Exponential Growth

b)

Exponential Decay

c)

Quadratic

10.

Describe the function.

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

11.

Describe the function.

a)

Exponential Growth

b)

Exponential Deacy

c)

Positive Linear

12.

Describe the function.

a)

Exponential Growth

b)

Exponential Decay

c)

Quadratic

13.

What is the Growth Factor of the equation.

$y\ =\ 5\left(3\right)^x$

14.

The graph for an exponential function is called a (a)

Choose from the below words

curve

line

parabola

15.

Match the following

a)

1.

Growth

b)

2.

Decay

c)

a

3.

y-intercept

d)

$y\ =\ ab^x$

4.

Exponential Function Equation

e)

b

5.

Growth/Decay Factor

16.

Describe the function. $y\ =\ 2\left(\frac{1}{2}\right)^x$

a)

Growth

b)

Deacy

17.

Describe the translation.

$y\ =\ 3^x+\ 2$

a)

Up 2

b)

Down 2

18.

Describe the function.

$y\ =\ 2\left(\frac{1}{2}\right)^x-\ 3$

Exponential function that goes (a) (b)

Choose from the below words

down

3 units

up

2 units

19.

if $y=2^x$ what is y when x = 0, 2, 4?

a)

1, 2 and 8

b)

1, 4 and 16

c)

0, 4 and 8

d)

1, 2 and 8

20.

Which of the following is an exponential function?

a)

y = x²

b)

f(x) = 3x³

c)

$y=\left(-2\right)^x$

d)

f(x) = 3^x

21.

Identify the asymptote of the function $-3\left(3\right)^x+4$

a)

y = -3

b)

y = 1

c)

y = 4

22.

Determine the range for the function

f(x) = 3(2)^x-4+ 5

a)

[5,∞)

b)

(5,∞)

c)

[4,∞)

d)

(4,∞)

23.

What is the range of this function?

a)

(-∞,0)

b)

(0,∞)

c)

(-∞,4)

d)

(4,∞)

24.

The parent function $f\left(x\right)=3^x$ is shown in red and is translated. What is the equation of the green graph?

a)

$g\left(x\right)=3^x+2$

b)

$g\left(x\right)=3^x-2$

c)

$g\left(x\right)=3^{x-2}$

d)

$g\left(x\right)=3^{x+2}$

25.

How has the function $7\left(3\right)^x-5$ been transformed from the parent function $7\left(3\right)^x$ ?

a)

Shifted up 5

b)

Shifted down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

26.

What is the domain of the function shown below?

a)

(-2,5)

b)

(0,12)

c)

$\left(0,\infty\right)$

d)

All Real Numbers

27.

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

28.

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

29.

Identify the initial value:

y = 6.87 (4)^x

a)

a = 4

b)

a = 6.87

c)

a = 3

d)

a = 1

30.

The function y = 125(1.13)^xrepresents Mr. Gantz's recent investments where x is measured in years. Which is NOT true?

a)

Mr. Gantz initial invested $125

b)

Mr. Gantz's money grows by 13% per year

c)

After 4 years Mr. Gantz will have about $203.81

d)

Mr. Gantz earns more money in year one than in year 5

31.

In an exponential function, what does the 'b' represent?

a)

Input

b)

Rate of change

c)

Y-intercept

d)

Output

32.

Which equation is represented by the table?

a)

y = 40(2)^x

b)

y = 40(1/2)^x

c)

y = 40 - 2x

d)

y = 40 - 1/2x

33.

Write the function for the following table:

a)

f(x) = 5x + .08

b)

f(x)= 5x + 2

c)

f(x) = .08(5)^x

d)

f(x)= 2(5)^x

34.

Write the function for the following table:

a)

f(x)= 1(2)^x

b)

f(x)= 2(1)^x

c)

f(x) = 2x+1

d)

f(x)= x+2

35.

Which table represents the following equation?

a)

b)

c)

d)

36.

Write an equations that models the data shown.

a)

$y=3x+6$

b)

$y=3\cdot2^x$

c)

$y=2x+3$

37.

What is the graph of the function

y=5\cdot2^x

a)

b)

c)

d)

38.

Suppose the population of a species of insects doubles every year. There are 1600 insects initially. The function for the scenario would be?

a)

$f\left(x\right)=2x+1600$

b)

$f\left(x\right)=1600\times2$

c)

$f\left(x\right)=1600\cdot2^x$

39.

The function

f(x)=1600\cdot2^x

gives the number of insects after x years. How many insects were there initially?

a)

1600

b)

2

c)

There is not enough information to tell.

40.

Use the function $m\left(t\right)=.05\left(2\right)^t$ where M is the amount of money you have after t days.

How much money will you have after 14 days?

a)

$ 819.20

b)

$ 1.4

c)

$ 140

41.

Use the function $n\left(t\right)=14000\left(.96\right)^t$ Where n is the number of employees and t is the number of years.

How many employees will there be after 3 years?

a)

14,000 employees

b)

12,386 employees

c)

40,360 employees

d)

15,748 employees

42.

An exponential function is graphed on the grid.

Which function is best represented by the graph?

a)

$p\left(x\right)=\left(0.25\right)^x$

b)

$p\left(x\right)=2\left(0.5\right)^x$

c)

$p\left(x\right)=\left(1.25\right)^x$

d)

$p\left(x\right)=\left(25\right)^x$

43.

The graph shows the number of game consoles sold in millions since 2009.

Based on this information, which function best models the number of game consoles sold in millions x years since 2009?

a)

$g\left(x\right)=0.6\left(25.5\right)^x$

b)

$g\left(x\right)=25.5\left(0.6\right)^x$

c)

$g\left(x\right)=6.12\left(25.5\right)^x$

d)

$g\left(x\right)=25.5\left(6.12\right)^x$

44.

Which variable represents time passed in the function y=ab^x?

a)

y

b)

a

c)

b

d)

x

45.

How do you write 5% as a decimal?

a)

50

b)

5

c)

0.5

d)

0.05

46.

Is this exponential growth or decay?

a)

Growth

b)

Decay

47.

Is this exponential growth or decay?

a)

Growth

b)

Decay

48.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

49.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

50.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

51.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

52.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

53.

Is y = 54(.20)^x growth or decay?

a)

Growth

b)

Decay

54.

Is y = -5(4)^x growth or decay?

a)

Growth

b)

Decay

55.

What is the range of y=2^x+1-3?

a)

(-∞,∞)

b)

(-3, ∞)

c)

(-1, ∞)

d)

(-∞, -3)

56.

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

a)

f(x)=400(1+3)^x

b)

f(x)=400(1-0.03)^x

c)

f(x)=400(1+0.03)^x

d)

f(x)=400(0.03)^x

57.

A new savings account is opened with $400 and gains 3% every yr. What's the amount after 5 years?

a)

$415

b)

$463.71

c)

$343.49

d)

$460.12

58.

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(0.92)^x

d)

y=15,000(0.08)^x

59.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the value after 7 years?

a)

$800

b)

$8367.70

c)

$6600

d)

$25,707.36

60.

What type of pattern do exponential functions have?

a)

Adds by the same number every time

b)

Multiplies by the same number every time

c)

Square roots all the inputs

d)

Squares all the inputs

61.

Which function will show exponential behavior?

F(x) = (4.3)^x

or

G(x) = 4.3x + 9

a)

F(x)

b)

G(x)

c)

both

d)

neither

62.

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

63.

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%

64.

The amount of downloads for an album on iTunes, g(d), where d is the number of days since the album was first uploaded can be represented as
g(d) = 5^1.5d
How many downloads will the album have after 3 days?

a)

125

b)

11

c)

1398

d)

140

65.

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

66.

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.

67.

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

68.

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

69.

Describe the equation
y = 100 * 2^x

a)

It starts with 100 and is tripling

b)

It starts with 100 and is doubling

c)

It starts with 2 and is being multiplied by 100 each time

d)

It starts with 100 and is adding 2 each time

70.

What is it about the equation y = 2(9/7)^x that indicates that it is a model for exponential growth?

a)

The equation is growth because 2 is positive.

b)

The equation is growth because the factor is positive.

c)

The equation is growth because the factor is greater than one.

d)

The equation is growth because the exponent is always positive.

71.

Consider the equation y=200(1.08)^x which models the increase in value of an autographed Annie program. Let y = the value of the item, let x = the number of years since the performance. What does the 1.08 in the equation indicate?

a)

The value of the item is increasing by $1.08 each year.

b)

The value of the item is increasing by 1.08% each year.

c)

The value of the item will increase to $200 1.08 years after purchase.

d)

The value of the item is increasing by 8% each year.

72.

What parts of an exponential equation could you find in a table?

a)

The factor is found as the first difference in the table, and the value of a is where y=0.

b)

The factor is found as the common ratio in the table, and the value of a is where y = 0.

c)

The factor is found as the common ratio in the table, and the value of a is where y = 0.

d)

The factor is found as the first difference in the table, and the value of a is where x=0.

Test 9: Exponential Functions REVIEW

Total questions: 72

Worksheet time: 3hrs 35mins

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