8.1 & 8.2 Exponential Functions 3/10/2014

In this lesson we will learn … What an exponential function is. Difference between exponential growth and decay. How to graph Exponential Growth and Exponential Decay functions.

Exponential Function Is a function written in the form: y = a·b x a is the initial amount b is the growth or decay factor

Exponential Growth Value of y increases (grows) as x increases When a ˃ 0 and b ˃ 1 Ex: y = 2 x where a =1 b =2 y = 2·3 x where a =2 b =3 y = ¼· 2 x where a =¼ b =2 Graphs: 1.Graph rises from left to right 2.As x decreases the graph gets closer to the x-axis. Exponential Decay Value of y decreases (decays) as x increases. When a ˃ 0 and b is between 0 and 1 Ex: y = (½) x where a =1 b = ½ y = 3·(¼) x where a =3 b =¼ Graphs: 1.Graph falls from left to right 2.As x increases the graph gets closer to the x-axis. Exponential Function y = a·b x 3. Domain (x-values) is all real numbers 4. Range (y-values) is all real numbers greater than 0

Graphing Exponential Functions

x x y x y a = 1 and b = 2 Since b > 1, the graph is Exponential Growth.

Graph y = 2 x xy=2 x -31/8 = ¼= 0.25 ½ =

x x y x y a = 1 and b = ½ Since 0<b < 1, the graph is Exponential Decay.

Graph x(½) x ½=0.5 2¼= /8=0.125

x x y Graph x y

Graph xy

x x y Graph x y

Graph xy

Homework: WS 8.1 & 8.2

Exponential Growth Graphs: Exponential Decay Graphs: Exponential Function y = a·b x