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EXAMPLE 6 Find the inverse of a power model Ticket Prices The average price P (in dollars) for a National Football League ticket can be modeled by P = 35t0.192 where t is the number of years since Find the inverse model that gives time as a function of the average ticket price.

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**Find the inverse of a power model**

EXAMPLE 6 Find the inverse of a power model SOLUTION P = 35t0.192 Write original model. = t0.192 p 35 Divide each side by 35. = (t0.192)1/0.192 p 35 1/0.192 Raise each side to the power 1 0.192 p 35 5.2 t Simplify. This is the inverse model.

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**Use an inverse power model to make a prediction**

EXAMPLE 7 Use an inverse power model to make a prediction Use the inverse power model from Example 6 to predict the year when the average ticket price will reach $58. SOLUTION t = P 35 5.2 Write inverse power model. = 58 35 5.2 Substitute 58 for P. ≈ 14 Use a calculator.

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EXAMPLE 7 Use an inverse power model to make a prediction ANSWER You can predict that the average ticket price will reach $58 about 14 years after 1995, or in 2009.

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**GUIDED PRACTICE for Examples 6 and 7**

11. Ticket Prices: The average price P (in dollars) for a Major League Baseball ticket can be modeled by P = 10.7t0.272 where t is the number of years since Write the inverse model. Then use the inverse to predict the year when the average ticket price will reach $25. SOLUTION P = 10.7t0.272 Write original model. = t0.192 p 10.7 Divide each side by 10.7.

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**GUIDED PRACTICE for Examples 6 and 7 p 1/0.272 = (t0. 272)1/0.272 10.7**

Raise each side to the power 1 0.272 3.68 t p 10.7 Simplify. This is the inverse model. Use the inverse power model from Example 6 to predict the year when the average ticket price will reach $58. t = P 10.7 3.68 Write inverse power model. = 25 10.7 3.68 Substitute 25 for P.

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**GUIDED PRACTICE for Examples 6 and 7 ≈ 25 ANSWER**

Use a calculator. ANSWER You can predict that the average ticket price will reach $25 about 23 years after 1995, or in 2017.

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