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

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

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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 =t = P = Write inverse power model. Substitute 58 for P. 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 Ticket Prices: The average price P (in dollars) for a Major League Baseball ticket can be modeled by P = 10.7t 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 Write original model. P = 10.7t Divide each side by = t p 10.7

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GUIDED PRACTICE for Examples 6 and 7 Raise each side to the power = (t ) 1/0.272 p /0.272 Simplify. This is the inverse model t p 10.7 Use the inverse power model from Example 6 to predict the year when the average ticket price will reach $58. t =t = P Write inverse power model. = Substitute 25 for P.

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GUIDED PRACTICE for Examples 6 and 7 25 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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