Mathematics 3201 – Ch. 6 - Exponential Functions Name:_________
Part 1. Multiple Choice. Circle the correct answer.
1. Which represents an increasing function?
A)
15
()
37
x
fx



B)
7
( ) 2
3
x
fx



C) f(x) = 2(1)
x
D)
1
( ) 0.3
2
x
fx
2. What is the y-intercept of: f(x) = 2(5)
x
?
A) (0, 2)
B) (0, 5)
C) (0, 10)
D) (0, 0)
3. Which exponential function represents the graph shown?
4. What is the range of f(x) = 3(0.5)
x
?
A) y > 0.5
B)
0.5y
C) y > 0
D)
0y
5. What is the domain of
3
( ) 2
4
x
fx



?
A)
2x
B)
C)
3
4
x
D)
0x
6. What is the exponential function for the data given:
x
-1
0
1
2
3
y
81
27
9
3
1
A)
1
27
3
x
y



B)
1
81
3
x
y



C)
 
27 3
x
y
D)
 
81 3
x
y
A)
( ) 3 2
x
fx
C
 
( ) 2 3
x
fx
B)
1
( ) 3
2
x
fx



D)
1
( ) 2
3
x
fx



x
- 5 - 4 - 3 - 2 - 1 1 2 3 4 5
y
- 1
1
2
3
4
5
6
7
8
9
7. Solve for x: 5
2x+1
= 125
3x
A)
1
8
B)
1
7
C)
1
4
D) 7
8. Solve for x:
4
28
x
A)
8
3
B)
3
8
C) 1
D)
1
8
9. Solve for x :
3( 2)
81 3
x
10. The function that models the growth of a bacteria
120
( ) 50(2)
t
At
where
A
(
t
) is the number of
bacteria present at time
t
, in minutes. Which statement is false?
A) The amount of bacteria doubles every 2 hours.
B) There are 50 bacteria present initially.
C) 100 will be present after 120 minutes.
D) 25 bacteria will be present in 2 hours.
11. A = 2500(1.12)
4
represents a bank loan that is compounded annually. What is the interest
rate?
12. Rick’s car is valued at $22,600 and depreciates in value by 16% per year. Which equation
represents the car’s value after 5 years?
13. Joel invested $5000 in a savings account that pays 6% annual interest compounded quarterly.
Which equation represents how much money Joel has after 6 years?
A)
10
3
B)
2
3
C)
3
5
D) 3
A) 2500%
B) 12%
C) 88%
D) 1.12%
A)
5
22600(1.16)V
B)
5
22600(0.16)V
C)
5
22600(0.84)V
D)
5
22600(1.84)V
A)
6
5000(1.015)V
B)
24
5000(1.015)V
C)
6
5000(0.94)V
D)
24
5000(0.94)V
1 2 3 4 5 6 7 8 9
x
1
2
3
4
5
6
7
8
9
10
y
14. A scatter plot is drawn using a data set. Identify the equation of the
curve of best fit.
Part 2: Answer all the questions showing all your work.
15. Solve each exponential equation. (11)
A)
3
1
1
125
25
x
x



B)
6
3
1
4
32
x
C)
147)7(3
53
x
A) f(x)= 4.8(1.08)
x
C) f(x) = 8.4(0.81)
x
B) f(x) = 4.8(0.81)
x
D) f(x) = 8.4(1.08)
x
18. Sam must choose between the following options for investing his $10,000 lottery prize for a
period of 5 years.
Option 1 – a mutual fund that promises 7.6% annual interest compounded bi-annually.
Option 2 – a mutual fund that promises 7.6% annual interest compounded monthly.
A) Write an equation to represent each option and use your equations to determine which
is the better deal for Sam.
(4)
B) What accounts for the different future values in this situation? Explain.
(1)
19. An element has a half-life of 45 years. If its initial mass is 8000 grams, algebraically determine
how long it will take to decrease to 1000 grams.
1
2
t
h
o
AA



(3)