2. What do you think of when you hear the word “exponential?”

3. 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?

4. 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

5. 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

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

7. Exponential Growth and Decay y = ab x Is b > 1? Then it’s a growth factor! Is 0 < b < 1? Then it’s a decay factor!

8. 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

9. What did you notice? Write a sentence!

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

11. Exponential Growth and Decay y = ab x a tells us the y- intercept If it’s negative, the graph becomes negative as well.

12. Who wants to act out an exponential function? The distance a frog can jump (y) each year (x) is modeled by the following equation: Starting with x=0, jump the distance y in feet. xy 0 1 2 3 4 5 6 7

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