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?

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 isY=3·2x

Write an Exponential function, y=abx whose graph goes thru

(-1,.0625) & (2,32)

• .0625=ab-1

• 32=ab2

•(.0625)=a/b•b(.0625)=a

•32=[b(.0625)]b2

•32=.0625b3

•512=b3

•b=8 a=1/2

y=1/2 · 8x

Modeling with POWER functions

•y = axb

• Only 2 points are needed

• (2,5) & (6,9)

• 5 = a 2b

• 9 = a 6b

a = 5/2b

9 = (5/2b)6b

9 = 5·3b

1.8 = 3b

log31.8 = log33b

.535 ≈ ba = 3.45y = 3.45x.535

• 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