Exponential and Logarithmic Functions

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.

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 = 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.

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 = 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.

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