§8.7 Exponential Functions
Objectives: SWBAT evaluate exponential functions
SWBAT graph exponential functions
Exponential Function—A function in the form 𝑓(𝑥) = 𝑎(𝑏)𝑥 , where a is a nonzero constant, b is
greater than zero and not equal to 1, and x is a real number
Example 1: Evaluate each exponential function for x = 0, 2, 3, 4
a 𝑓(𝑥) = 2(5)𝑥 )
1
b) 𝑓(𝑥) = 2 (2)𝑥
3 𝑥
c) 𝑓(𝑥) = −3 (2)
Example 2: Suppose 20 rabbits are taken to an island. The rabbit population triples every halfyear. The function 𝑓(𝑥) = 20(3)𝑥 , where x is the number of half-year periods, models the
situation. How many rabbits would there be after 2 years? After 4 years?
Example 3: Suppose 10 mice are taken to an island. Their population quadruples every year.
Write a model to represent the number of mice after x years. How many mice will there be after
5 years?
Graphing Exponential Functions
Based on these graphs, what generalizations can you make about the graphs of exponential
functions?
Example 4: Graph each exponential function.
a) 𝑓(𝑥) = 2(3)𝑥
b) 𝑓(𝑥) = −2(3)𝑥
Example 5: Many photocopiers allow you to choose how large you want your image to be. The
function 𝑓(𝑥) = 1.5𝑥 models the new size of an image being copied over and over at 150%,
where x is the number of enlargements. Graph the function.
Example 6: You can also make images that are smaller than the original on a photocopier. The
function 𝑓(𝑥) = 0.9𝑥 models the new size of an image being copied over and over at 90%.
Graph the function.
Are the graphs in example 4, 5 and 6 discrete or continuous? Explain your answer.
Name
Class
Date
Practice 8–7
Exponential Functions
Complete the table for each exercise.
1.
2.
3.
Evaluate each function for the domain {–2, 0, 1, 2, 4}.
4.
y = 2x
5.
y = 3.1x
6. y = 0.8x
7.
y = 2  4x
8.
y = 10  3x
9. y = 25  5x
10. y =
 2
 
 3
x
11. y = 100 
1
 
 10
x
12. y =
1  8x
4
Graph each function.
13. y = 3x
14. y = 6x
15. y = 1.5x
16. y = 7x
17. y = 10  5x
18. y = 16  0.5x
20. y = 1  4x
21. y = 8   5 
2
19. y =
1
8
 2x
2
x
 
Evaluate each function rule for the given values.
22.
y = 5.5x for x = 1, 3, and 4
23.
y = 4  1.5x for x = 2, 4, and 5
24.
y = 3  4x for x = 1, 3, and 5
25.
y = 6x for x = 2, 3, and 4
26.
y = 0.7x for x = 1, 3, and 4
27.
y = 3.1x for x = 1, 2, and 3
28.
y = 180  0.5x for x = 0, –2, and  1
29.
y = 4.3x for x = –2, –1, and 0
y = 100  0.1x for x = –4, –1, and 2
31.
y = 5x for x = –2, –3, and 4
2
30.
Solve each equation.
32.
5x = 625
33.
2  4x = 128
34.
4x = 1
35.
4  5x =
64
4
125