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8.7

8.7. Modeling with Exponential and Power Functions. Learning Targets. Students should be able to… Model data with exponential functions. Model data with power functions. Warm-up. Homework Check. Writing Exponential Functions. General form of an EXPONENTIAL FUNCTION: y = ab x.

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8.7

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  1. 8.7 Modeling with Exponential and Power Functions

  2. Learning Targets • Students should be able to… • Model data with exponential functions. • Model data with power functions.

  3. Warm-up

  4. Homework Check

  5. Writing Exponential Functions General form of an EXPONENTIAL FUNCTION: y = abx

  6. Write an exponential function whose graph passes through each of the two given points. • (1, 3) and (2, 36) b = 12 a = 3/12 = 1/4 y = ¼(12)x

  7. 2) (2, 18) and (3, 108) b = 6 a = 18/36 = 1/2 y = ½ (6)x

  8. Finding an Exponential Model • The table below gives the number of years, t, since buying a car and its trade-in value, V, in dollars. Find an exponential model for the data. 1. Type the table into L1 andL2 on your calculator. 2. Calc: Stat, Calc, ExpReg L1, L2 Y = 12957.03(.701)x

  9. Writing Power Functions General form of a POWER FUNCTION: y = axb Recall Change of Base Formula:

  10. Write a power function whose graph passes through each of the two given points. • (2, 1) and (6, 9) b = 2 a = 1/4 y = ¼(x2)

  11. 2) (6, 8) and (12, 36) b = 2.17 a= .164 y = .164x2.17

  12. Finding a Power Model • Write a power model to represent the data below. 1. Type the table into L1 andL2 on your calculator. 2. Calc: Stat, Calc, PwrReg L1, L2 y = .998x2.3

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