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

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?

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

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

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

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!

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

What did you notice? Write a sentence!

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

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

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

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