1. Graphs of Exponential Functions
Lesson 3.3

2. -5<x<5 -10<y<10
How Does a*bt Work?
Given f(t) = a * bt
What effect does the a have?
What effect does the b have?
Try graphing the following on the same axes 3 * 1.1X * 1.1X 2 * 1.1X * 1.1X 1.5 * 1.1X
Set the window at
-5<x<5 -10<y<10

3. How Does a*bt Work? Conclusion All the graphs cross the y-axis at A
The graph is steeper for some x

4. How Does a*bt Work?
Now let’s try to see what happens when we change the value for b
Specify the following in the Y= screen 2*1.1x 2*1.5x 2*2.0x 2*2.5x
Verify conclusions with spreadsheet from previous lesson.
Set the window at
-5<x<5 -10<y<10

5. How Does a*bt Work? Results: All graphs cross the y-axis at y=2
If b is low: high to left, shallow up to right
If b is large: low to the left, steeper sooner on the right

6. -5<x<5 -10<y<10
How Does a*bt Work?
Consider 0 < b < 1
Graph the following: 2*0.75x 2*0.5x 2*0.25x 2*0.1x
Set the window at
-5<x<5 -10<y<10

7. How Does a*bt Work? Results when 0 < b < 1
Graph is up to the left, down to the right

8. Assignment A
Lesson 3.3A
Page 127
Exercises 1 – 25 odd

9. Horizontal Asymptotes
When b > 1, f(x) 0 as x  -∞
When 0 < b < 1, f(x) 0 as x +∞
View Nspire demo

10. Restrictions on b Note always b > 0 … cannot have
Fractional power of b when b < 0
It is not a continuous function
Also note that calculator will do some funny things with y = (-2)^x
???

11. Sales of Compaq Revenue from Compaq Computers
Use your calculators to determine an exponential regression modeling function

12. Assignment
Lesson 3.3B
Page 128
Exercises 27 – 41 odd