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Exponential Function Practice

Total questions: 46

Worksheet time: 2hrs 1mins

Name
Class
Date
1.

What is the common ratio of the following geometric sequence:

3, 15, 75, 375

a)

r = 3

b)

r = 5

c)

r = 6

d)

r = 375

2.

What is the 9th term of the following geometric sequence:

3, 15, 75, 375

a)

1875

b)

9375

c)

234,375

d)

1,171,875

3.

What is the 11th term of the following geometric sequence:

5, 7.5, 11.25, ...

a)

288.325

b)

16.875

c)

25.313

d)

85.430

4.

What does the graph represent?

a)

Exponential Decay

b)

Exponential Growth

5.

What does this graph represent?

a)

Exponential Decay

b)

Exponential Growth

6.

What is the initial value of the situation represented by f(x)=0.05(2)x?

a)

0.05

b)

2

c)

0.1

d)

1

7.

This is the horizontal line which the values of the function cannot fall below :

a)

Asymptote

b)

Growth Factor

c)

Axis of symmetry

d)

Curve

8.

Is the following function and example of decay or growth?

f(x)=2(0.85)x

a)

Exponential Decay

b)

Exponential Growth

9.

Is the following function an example of decay or growth?

f(x) = 2(1.25)x

a)

Exponential Growth

b)

Exponential Decay

10.
Is the graph linear, exponential or neither?
a)
Linear
b)
Exponential
c)
Neither
11.
In an exponential function, what does the 'a' represent? 
a)
SLOPE
b)
RATE OF CHANGE
c)
Y-INTERCEPT
d)
COMMON RATIO
12.

What is the initial value for the function: f(x) = 300(1.16)x?

a)

300

b)

1.16

c)

.16

d)

x

13.
A population of 2200 beetles is too large to sustain and decreases in population each month at a rate of 5%. How would you write your decay factor, b?
a)
-5
b)
-.05
c)
.95
d)
.05
14.
The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?
a)
.08
b)
1.08
c)
.92
d)
8
15.
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
16.
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
17.
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
18.
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
19.
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%
20.
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
21.
What is the y-intercept of the function?
a)
2
b)
3
c)
1
d)
-2
22.

The function given is an example of growth or decay?

 y=3⋅(12)xy=3\cdot\left(\frac{1}{2}\right)^x  

a)

Growth

b)

Decay

23.
Write the equation of the function. 
a)
y=-3x+6
b)
y=6x-3
c)
y=1.96 ⋅ 1.89x
d)
y=1.89 ⋅ 1.96x
24.
Determine whether each table or rule represents a linear or an exponential function.
a)
Linear 
b)
Exponential 
25.
Determine whether each table or rule represents a linear or an exponential function.
a)
Linear 
b)
Exponential 
26.
Write the equation of the function. 
a)
y=11.49x-19.2
b)
y=-19.2x+11.49
c)
y=2⋅1x
d)
y=1⋅2x
27.
Determine whether each table or rule represents a linear or an exponential function.
a)
Linear 
b)
Exponential 
28.
Write the equation of the function.
a)
y=-2x+3
b)
y=3x-2
c)
y=1.05 ⋅1.66x
d)
y=1.66 ⋅1.05x
29.
Determine whether each table or rule represents a linear or an exponential function.
a)
Linear 
b)
Exponential 
30.
Write the equation of the function.
a)
y=25.2x-33
b)
y=-33x+25.2
c)
y=3⋅1x
d)
y=1⋅3x
31.

What is the growth rate of this model?

a)

1.12

b)

112%

c)

12%

d)

5000

32.

What is the starting population?

a)

.955

b)

4.7

c)

there is no population yet, this happens in the future

d)

How am I supposed to know this?

33.

Which of the following could be the equation for this graph?

a)
b)
c)
d)
34.

The population of a country is 50 millions of inhabitants. If it grows exponentially in a rate of 2% per year, calculate the estimated population in 15 years

a)

1.02 million people

b)

6 years

c)

3.5 years

d)

67.3 million people

e)

2%

35.
Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. If no other money is added or withdrawn from the account, how much will be in the account after 10 years?
a)
$3122.18
b)
$4994.50
c)
$4440.73
d)
$86,776.40
36.
A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?
a)
14327
b)
4309
c)
839
d)
7680
37.
Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?
a)
$4915.59
b)
$3933.28
c)
$2979.81
d)
$4005.09
38.
The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.
a)
y=1400(1.09)x
b)
y=1.09(1400)x
c)
y=1400(.91)x
d)
y=1.09x
39.

Andy invests $500 into an account with 4.8% interest, compounded monthly. How much will be in the account in 10 years?

a)

$799.06

b)

$520.36

c)

$807.26

d)

$877.61

40.
a)
b)
c)
d)
41.
a)
b)
c)
d)
42.
a)
b)
c)
d)
43.
a)
b)
c)
d)
44.
a)
b)
c)
d)
45.
Simplify the exponential expression:
a)
10x-2
b)
2x2
c)
2x12
d)
10x12
46.
Simplify the following exponential expression:
(3x4)(5x3)
a)
15x12
b)
8x7
c)
8x12
d)
15x7

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