1. 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?

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

3. 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:

4. 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

5. 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

6. 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

7. 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.

8. 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

9. Homework
Page 513
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