1. Check Skills/Warm Ups Graph each function.
1. y = 3x 2. y = 4x 3. y = –2x
Simplify each expression.
– • 34
7. 2 • 3– • 2– • 32

2. Solutions
1. y = 3x  
2. y = 4x  
3. y = –2x 
4. 32 = 3 • 3 = –3 = = =
6. 2 • 34 = 2 • (3 • 3 • 3 • 3) = 2 • 81 = 162
7. 2 • 3–2 = 2 • = = 𝟐 𝟗
3 • 2-1 = 3 • = 𝟑 𝟐 or 𝟏 𝟏 𝟐
10 • 32 = 10 • (3 • 3) = 10 • 9 = 90 1 53 1
5 • 5 • 5 1
125

3. Homework Solutions 2. 1 32. − 27 8 20. 1  10–12 s 46. 𝑡 6 27 4. 0
2. 1
4. 0
6. 4
8. m3
10. y
12. 𝑡 𝑚 4
14. 3  10–5
 103
7  10–3
20. 1  10–12 s
𝑥 3
𝑎 𝑏 4 𝑝
32. − 27 8
𝑛 3
36. 1
𝑚 12
45. 𝑎 6
𝑡 6 27
𝑎 4 4𝑏 10
𝑎 5 𝑐 5 𝑏 3
56. 𝑟 5 𝑝 25 𝑞 5
𝑏 5 5𝑎

4. 8-7: Exponential Functions
Objectives:
To evaluate exponential functions.
To graph exponential functions.

5. Key Concepts:
Exponential Function: a function that repeatedly multiplies an initial amount by the same positive number.

6. Example 1: Evaluate each exponential function.
a. y = 3x for x = 2, 3, 4
x y = 3x y
2 32 = 9 9
3 33 = 27 27
4 34 = 81 81
b. p(q) = 3 • 4q for the domain {–2, 3}
q p(q) = 3 • 4q p(q)
–2 3 • 4–2 = 3 • = 1 16 3
3 3 • 43 = 3 • 64 =

7. Example 2:
Suppose two mice live in a barn. If the number of mice quadruples every 3 months, how many mice will be in the barn after 2 years?
ƒ(x) = 2 • 4x
ƒ(x) = 2 • 48
In two years, there are 8 three-month time periods.
ƒ(x) = 2 • 65,536
Simplify powers.
ƒ(x) = 131,072
Simplify.

8. Try These: Evaluate each function rule for the given value.
a.  y = 0.5x for x = 3
b.  ƒ(x) = 4 • 3x for x = –2
0.125
4 9

9. Example 3: Graph y = 2 • 3x. x y = 2 • 3x (x, y) –2 2 • 3–2 = = (–2, )
2 2 • 32 = 2 • 9 = 18 (2, 18)
x y = 2 • 3x (x, y)
–2 2 • 3–2 = = (–2, ) 2
3 2 9
–1 2 • 3–1 = = (–1, ) 2 31 3
0 2 • 30 = 2 • 1 = 2 (0, 2)
1 2 • 31 = 2 • 3 = 6 (1, 6)

10. Example 4:
The function ƒ(x) = 1.25x models the increase in size of an image being copied over and over at 125% on a photocopier. Graph the function.
x ƒ(x) = 1.25x (x, ƒ(x))
= (1, 1.3)
= (2, 1.6)
= (5, 3.1)
= (4, 2.4)
= (3, 2.0)

11. Try These: Suppose an investment of $5000 doubles every 12 years.
a.  How much is the investment worth after 24 years?
b.  After 48 years?
$20,000
$80,000
4. Graph y = –0.5 • 3x.
3. Graph y = 0.5 • 3x.

12. HW #42: p. 435 #1-10 (correct in class) Quiz 8B Tomorrow: 8.4, 8.5, 8.6 HW #43: p. 432 #1-18