1. Exponential Functions

2. Exponential Functions
An exponential function is a function with the general form: y = a(b)x
where a doesn’t equal 0, and b is positive and not equal to 1.
What do a and b mean?
Be sure to emphasize that students must write down the general form of an exponential equation.

3. Graph the following in your calculator and draw a quick sketch of what you see. What’s happening?
1. y = 1(2)x 2. y = 1(5)x 3. y = 1(15)x

4. Graph the following in your calculator and draw a quick sketch of what you see. What’s happening?
1. y = 1(.8)x 2. y = 1(.5)x 3. y = 1(.1)x

5. Can you write a sentence about y = a(b)x that explains what you just discovered?

6. Exponential Growth and Decay
y = abx
Is b > 1? Then it’s a growth factor!
Is 0 < b < 1? Then it’s a decay factor!
Make sure to give students ample time to write down the fact that b must be greater than 1 in order for the function to represent exponential growth.

7. Graph the following in your calculator and draw a quick sketch of what you see. What’s happening?
1. y = 1(3)x 2. y = 5(3)x 3. y = 10(3)x

8. What did you notice? Write a sentence!

9. What do you suspect will happen here?
1. y = -1(3)x 2. y = -5(3)x 3. y = -10(3)x

10. Exponential Growth and Decay
y = abx
a tells us the y-intercept
If it’s negative, the graph becomes negative as well.
Make sure to give students ample time to write down the fact that b must be greater than 1 in order for the function to represent exponential growth.

11. Let’s discuss!
What are some real world examples of exponential growth and decay?