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8.7 Modeling with Exponential & Power Functions

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.

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8.7 Modeling with Exponential & Power Functions

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  1. 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?

  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,.0625) & (2,32) • .0625=ab-1 • 32=ab2 • (.0625)=a/b • 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 • 17-22, 29-35

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