1. 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.

2. 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.

3. 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.

4. 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.

5. 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.
ANSWER
t = P
10.7
3.68
; 2017.