EXAMPLE 6

1. Ticket Prices 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 = 35t0.192 where tis the number of years since 1995. Find the inverse model that gives time as a function of the average ticket price.

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

3. 5.2 t= P 58 35 35 5.2 = 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 Write inverse power model. Substitute 58 for P. ≈ 14 Use a calculator.

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

5. p 10.7 = t0.192 for Examples 6 and 7 GUIDED PRACTICE 11. Ticket Prices: The average price P(in dollars) for a Major League Baseball ticket can be modeled by P = 10.7t0.272 where tis the number of years since 1995. 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. Divide each side by 10.7.

6. P 3.68 t= 10.7 3.68 = Raise each side to the power . 25 10.7 t 1 0.272 p p 1/0.272 = (t0. 272)1/0.272 10.7 10.7 3.68 for Examples 6 and 7 GUIDED PRACTICE 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. Write inverse power model. Substitute 25 for P.

7. ANSWER You can predict that the average ticket price will reach $25 about 23 years after 1995, or in 2017. for Examples 6 and 7 GUIDED PRACTICE ≈ 25 Use a calculator.