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7.7: Write and Apply Exponential and Power Functions

7.7: Write and Apply Exponential and Power Functions. Objectives: Write and solve exponential and power functions. Transform exponential and power functions by changing parameters. Common Core Standards: F-BF-1, F-BF-5, F-LE-2, F-LE-4, S-ID-6 Assessments :

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7.7: Write and Apply Exponential and Power Functions

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  1. 7.7: Write and Apply Exponential and Power Functions Objectives: Write and solve exponential and power functions. Transform exponential and power functions by changing parameters. Common Core Standards: F-BF-1, F-BF-5, F-LE-2, F-LE-4, S-ID-6 Assessments: Define all Vocab for this section Do worksheet 7-7 Vocabulary Quiz Tomorrow!

  2. x Write an exponential function y = abwhose graph passes through (1, 12) and (3, 108). EXAMPLE 1

  3. Scooters A store sells motor scooters. The table shows the number yof scooters sold during the xth year that the store has been open. Find an exponential model EXAMPLE 2 • Draw a scatter plot of the data pairs (x, lny). Is an exponential model a good fit for the original data pairs (x, y)? • Find an exponential model for the original data.

  4. Enter the original data into a graphing calculator and perform an exponential regression. The model is y = 8.46(1.42) . x Substituting x = 8(for year 8) into the model gives y = 8.46(1.42)140scooters sold. 8 Use exponential regression EXAMPLE 3 SOLUTION

  5. Find an exponential model. Y=abxby solving for y. • Ln y= 1.024x + 1.668 • y= e1.024x + 1.668 • y= e1.668 * (e1.024)x • y= 5.3(2.78)x

  6. Find an exponential model. Y=abxby solving for y. • ln y = 2x + 1

  7. Power Function • A power function has the form y= axb where a is a real number and b is rational. • Because there are only two constants (a and b), only two points are needed to solve.

  8. b Write a power function y = axwhose graph passes through (1, 2) and (2, 32) . Write a power function EXAMPLE 4 Substitute the coordinates of the two given points into y = axb.

  9. Write a power function y = axbwhose graph passes through (1, 2)and (7, 6) .

  10. The table at the right shows the typical wingspans x(in feet) and the typical weights y(in pounds) for several types of birds. • 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.

  11. Use power regression EXAMPLE 6 Use a graphing calculator to find a power model for the data in Example 5. Estimate the weight of a bird with a wingspan of 4.5 feet.

  12. Find a power model (y=axb) by solving for y. • Ln y = 7 ln x

  13. Find a power model (y=axb) by solving for y. • ln y = 4.1 ln x + 1.4

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