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8.7 Modeling with Exponential & Power Functions p. 509 How do you write an exponential function given two points? How do you write a power function given two points? Which function uses logs to solve it?

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Just like 2 points determine a line, 2 points determine an exponential curve.

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Write an Exponential function, y=ab x whose graph goes thru (1,6) & (3,24) Substitute the coordinates into y=ab x to get 2 equations. 1. 6=ab =ab 3 Then solve the system:

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Write an Exponential function, y=ab x whose graph goes thru (1,6) & (3,24) (continued) 1. 6=ab 1 a=6/b 2. 24=(6/b) b 3 24=6b 2 4=b 2 2=b a= 6/b = 6/2 = 3 So the function is Y=3·2 x

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Write an Exponential function, y=ab x whose graph goes thru (-1,.0625) & (2,32).0625=ab -1 32=ab 2 (.0625)=a/b b(.0625)=a 32=[b(.0625)]b 2 32=.0625b 3 512=b 3 b=8 a=1/2 y=1/2 · 8 x

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Modeling with POWER functions y = ax b Only 2 points are needed (2,5) & (6,9) 5 = a 2 b 9 = a 6 b a = 5/2 b 9 = (5/2 b )6 b 9 = 5·3 b 1.8 = 3 b log = log 3 3 b.535 b a = 3.45 y = 3.45x.535

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You can decide if a power model fits data points if: (lnx,lny) fit a linear pattern Then (x,y) will fit a power pattern See Example #5, p. 512 You can also use power regression on the calculator to write a model for data.

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How do you write an exponential function given two points? y = ab x How do you write a power function given two points? y = ax b Which function uses logs to solve it? Power function y = ax b

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Homework Page , 29-35

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