8-6: Write and Solve Exponential Decay and Functions By: Dazha, Joe, and Elizabeth.

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8-6: Write and Solve Exponential Decay and Functions By: Dazha, Joe, and Elizabeth

Vocabulary Exponential decay- when a>0 and 0<b<1, the function y=ab^x.

Procedures (Graphing) Write out table with the domain as -2,- 1,0,1,2(Or any other numbers, -2 through 2 are recommended.) Plug in each domain in equation y=ab^x with the domain representing x. (ab will usually be fraction) Every time 0 will have a range of 1. Plot points on graph. Graph should have a downward curve going from left to right once completed.

Example. y=5*(1/4)^x Plug in the top(y) numbers for x. Now plot these points on graph (y) (x)

Example y=(3/5)^x Plug in top numbers(y) for x). Now plot numbers on graph.

Example y=(.25)^x Plug in top numbers (y) into x. Plot points on graph.

x Y=(1/2)^x Y=3*(1/2)^xY=- 1/3*(1/2)^x /3 26-2/ /3 11/23/2-1/6 21/43/4-1/12 Graph the functions y= 3*(1/2)^x. Compare each graph with the graph of y= (1/2)^x. Because the y-values for y=3* (1/2)^x are 3 times the corresponding y-values for the y=(1/2)^x, the graph of y= 3*(1/2)^x is a vertical stretch of the graph of y=(1/2)^x. Because the y-values for y=-1/3*(1/2)^x are -1/3 times the corresponding y-values for y=1/2^x, the graph of y= -1/3*(1/2)^x is a vertical shrink with reflection in the x-axis f the graph of y=(1/2)^x. Compare the lines by graphing.

Example Tell whether the table represents an exponential function. If so, write a rule. X-2012 Y1/271/91/ *3 *3 X-Values: increase by one. Y-values: multiply by three. The top of the table (x-values), always add or subtract. The bottom of the table (y-values), always multiply or divide. Zero will always have an answer of one but becomes 1/3 when the y- values are multiplied by three Y=ab^x Change in the graph/ rule. Y-intercept A= 1/3 (Rule) B=3