1. 8.1 & 8.2 Exponential Growth and Decay 4/16/2012

2. 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

3. Exponential Growth When a ˃ 0 and b ˃ 1 Value of y increases as x increases 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 When a ˃ 0 and b is between 0 and 1 Value of y decreases as x increases 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. Graph passes through (0, a) and (1, a·b) 4. Domain (x-values) is all real numbers 5. Range (y-values) is all real numbers greater than 0

4. Graph y = 2 x xy=2 x -31/8 = 0.125 -2¼= 0.25 ½ = 0.5 01 12 24 38

5. Graph x(½) x -38 -24 2 01 1½=0.5 2¼=0.25 31/8=0.125