4.7 Write and Apply Exponential

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4.7 Write and Apply Exponential Power Functions

• p. 509
• How do you write an exponential function given
  two points?

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Just like 2 points determine a line, 2 points
determine an exponential curve.An Exponential
Function is in the form of yabx
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Write an Exponential function, yabx whose graph
goes thru (1,6) (3,24)

• Substitute the coordinates into yabx to get 2
  equations.
• 1. 6ab1
• 2. 24ab3
• Then solve the system

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Write an Exponential function, yabx whose graph
goes thru (1,6) (3,24) (continued)

• 1. 6ab1 ? a6/b
• 2. 24(6/b) b3
• 246b2
• 4b2
• 2b

a 6/b 6/2 3
So the function is Y32x
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SOLUTION
STEP 1
Substitute 12 for y and 1 for x.
Substitute 108 for y and 3 for x.
STEP 2
 
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Simplify.
 
Divide each side by 12.
 
Take the positive square root because b gt 0.
 
STEP 3
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Write an Exponential function, yabx whose graph
goes thru (-1,.0625) (2,32)

• .0625ab-1
• 32ab2

• (.0625)a/b
• b(.0625)a

• 32b(.0625)b2
• 32.0625b3
• 512b3
• b8

y1/2 8x
a1/2
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4.7 Assignment

• Page 285, 3-8 all

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Power Function

• A Power Function is in the form of y axb
• Because there are only two constants (a and b),
  only two points are needed to determine a power
  curve through the points

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4.7 Write and Apply Exponential Power
Functions- Day 2
p. 509 How do you write a power function given
two points? Which function uses logs to solve it?
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Modeling with POWER functions
a 5/2b 9 (5/2b)6b 9 53b 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

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SOLUTION
STEP 1
Substitute 2 for y and 3 for x.
Substitute 9 for y and 6 for x.
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STEP 2
Simplify.
Divide each side by 2.
Change-of-base formula
Use a calculator.
STEP 3
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6. (3, 4), (6, 15)
SOLUTION
STEP 1
Substitute 4 for y and 3 for x.
Substitute 15 for y and 6 for x.
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STEP 2
Simplify.
Divide each side by 4.
3.7 2
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Change-of-base formula
Simplify.
Use a calculator.
STEP 3
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Biology page 284
Draw a scatter plot of the data pairs (ln x, ln
y). Is a power model a good fit for the original
data pairs (x, y)?
Find a power model for the original data.
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• 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

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Homework

• Page 285
• 15-20