Graphing Exponential Growth and Decay An exponential function

Graphing Exponential Growth and Decay

An exponential function has the form b is a positive number other than 1. If b is greater than 1 (fraction) If b is between 0 and 1 b is the “growth factor” Is called an exponential growth function. b is the “decay factor” Is called an exponential decay function.

Growth or decay? ? a = _______ b = _______

4 Shapes of Exponential Graphs

Graph y = bx for b > 1 x Graph y = 2 +0 1. Draw the asymptote 2. Make a table of values.

EXAMPLE 2 x Graph y = ab for b > 1 Graph the function. 1. Draw the asymptote 2. Plot 0, 1 and (1, 2) 2 draw a curve that “hugs” the x-axis, and moves up to the right. Just use 2 values in your table! x 0 1 y ½ 2

x EXAMPLE 3 Graph y = ab for b > 1 Graph the function. y= – 5 2 x Draw the asymptote Plot (0, – 1) and 1, – 5. 2 Draw a curve that begins just below the x-axis, and moves down to the right. Just use 2 values in your table! x 0 y -1 1 -5/2

EXAMPLE 4 Graph y = ab x for 0 < b < 1 Graph the function. 1 x Graph y = 2 4 +1 Draw the asymptote Plot (0, 3) and 1, 3. 2 draw a curve that begins just above the x-axis and moves up to the left. Just use 2 values in your table! x y 0 3 1 3/2

EXAMPLE 5 Graph y = ab x for 0 < b < 1 Just use 2 values in your table! 2 x Graph y = – 3 5 -2 Draw the asymptote Plot (0, – 5) and 1, – 3. 2 Draw a curve that begins just below the x-axis, and moves down to the left. x 0 y -5 1 -3. 2