Free Printable Lab 18 Basics of Exponential Functions

1.

What type of function is f(x)=2(1/7)^x ?

a)

Exponential Growth

b)

Linear

c)

Exponential Decay

d)

None of the Abovee

2.

Is this exponential growth or decay?

a)

Growth

b)

Decay

3.

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

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

4.

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

5.

What is the x-intercept of the exponential function?

a)

(0,1)

b)

(0,0)

c)

There is not one

6.

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

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

7.

What is the common ratio for the sequence:
28, 14, 7, 3.5...

a)

2

b)

1/2

c)

-14

d)

-7

8.

Identify the y-intercept (initial value) of the function f(x)=2(4)^x.

a)

2

b)

4

c)

(2)^x

d)

8

9.

True or False: This is an exponential function.

a)

True

b)

False

10.

True or False: This is an exponential function.

a)

True

b)

False

11.

Which function models this table?

a)

$f\left(x\right)=2\cdot4^x$

b)

$f\left(x\right)=4^x$

c)

$f\left(x\right)=4\cdot2^x$

d)

$f\left(x\right)=8^x$

12.

What is $\frac{1}{100}$ written as a single power?

a)

$10^2$

b)

$10^1$

c)

$10^{-2}$

d)

$10^{-3}$

13.

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.

14.

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

15.

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%

16.

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. Suppose f(20) = 49. Which of the following is true?

a)

After 20 days, there are 49 ants in the colony.

b)

After 49 days there are 20 ants in the colony.

c)

The amount of ants times 20 is 49.

d)

After 20 days the amount of ants remaining decreases by 49.

17.

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

18.

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

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.
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.

21.

Is the graph exponential growth or decay?

a)

Exponential growth

b)

Exponential decay

22.

Is the following function exponential growth, exponential decay, linear, or none of the above.
g(x) = 740(.001)^3x

a)

Exponential growth

b)

Exponential decay

c)

Linear

d)

None of the above

23.

Is the following function exponential growth, exponential decay, linear, or none of the above?
p(x) = 13x - 5

a)

Exponential growth

b)

Exponential decay

c)

Linear

d)

None of the above

24.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

25.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

26.

Which equation matches the graph?

a)

y = 2^x+3

b)

y = 2^x + 3

c)

y = 2^x

d)

y = 2^-x

27.

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

a)

Growth

b)

Decay

28.

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

a)

Growth

b)

Decay

29.

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

a)

(-∞,∞)

b)

(-3, ∞)

c)

(-1, ∞)

d)

(-∞, -3)

30.

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

31.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

32.

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

33.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

34.

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

a)

Growth

b)

Decay

35.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

36.

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

37.

Given y=3^xdetermine the y-intercept

a)

1

b)

3

c)

0

d)

y

38.

What is the asymptote of this function?

a)

y = 0

b)

y = 5

c)

y = 2

d)

y = 1

39.

Pick the equation that is exponential decay

a)

y = 2000(0.88)^x

b)

y = 0.5(1.88)^x

c)

y = 10(3/2)^x

d)

y = 0.8(13)^x

40.

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

41.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

42.

Solve for x:
9^x+8= 81

a)

2

b)

-6

c)

6

d)

8

43.

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

44.

Given the following 2 points on an exponential graph, write the exponential equation by finding b and then a, both to the nearest hundredth. The points are (

a)

$y=\left(2\right)\left(5\right)^x$

b)

$y=\left(5.02\right)\left(1.48\right)^x$

c)

$y=\left(5.01\right)\left(1.49\right)^x$

45.

$y=32\left(\frac{1}{2}\right)^x$ For this exponential equation what is the horizontal asymptote?

a)

y=32

b)

y=1/2

c)

y=0

d)

y=10

46.

$y=32\left(\frac{1}{2}\right)^x+10$ For this exponential equation what is the horizontal asymptote?

a)

y=32

b)

y=1/2

c)

y=0

d)

y=10

47.

$f\left(x\right)=5\left(2\right)^x$ Is this exponential equation represent growth or decay?

a)

growth

b)

decay

48.

$y=5\left(2\right)^{-2x}$ Is the exponential equation a growth or decay curve? (Hint: rewrite the base and exponent so the exponent is positive)

a)

growth

b)

decay

49.

All of the exponential equations below have the same base of 1/4 (some need to be rewritten) except which equation?

a)

$y=3\left(4\right)^{-x}$

b)

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

c)

$y=3\left(1.25\right)^x$

d)

$y=3\left(.25\right)^x$

50.

True or False? An exponential equation is a one to one function?

a)

False

b)

True

Lab 18 Basics of Exponential Functions

Total questions: 50

Worksheet time: 4hrs 10mins

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