8.7 Modeling with Exponential & Power Functions

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8.7 Modeling with Exponential & Power Functions
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?

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

Write an Exponential function, y=abx whose graph goes thru (1,6) & (3,24)
Substitute the coordinates into y=abx to get 2 equations. 1. 6=ab1 2. 24=ab3 Then solve the system:

Write an Exponential function, y=abx whose graph goes thru (1,6) & (3,24) (continued)
1. 6=ab1 → a=6/b 2. 24=(6/b) b3 24=6b2 4=b2 2=b a= 6/b = 6/2 = 3 So the function is Y=3·2x

Write an Exponential function, y=abx whose graph goes thru (-1,
b(.0625)=a 32=[b(.0625)]b2 32=.0625b3 512=b3 b=8 y=1/2 · 8x a=1/2

Modeling with POWER functions
a = 5/2b 9 = (5/2b)6b 9 = 5·3b 1.8 = 3b log31.8 = log33b .535 ≈ b a = 3.45 y = 3.45x.535 y = axb Only 2 points are needed (2,5) & (6,9) 5 = a 2b 9 = a 6b

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.

How do you write an exponential function given two points?
y = abx How do you write a power function given two points? y = axb Which function uses logs to solve it? Power function y = axb

Homework Page 513 17-22, 29-35