The average ticket price P at movie theaters from 2001 through 2014 can be approximated by the model
P = −0.0038t2 + 0.272t + 5.25, 1 ≤ t ≤ 14
where t represents the year, with t = 1 corresponding to 2001. (Source: National Association of Theatre Owners)
(a) Use a graphing utility to graph the model. Then use the graph to determine the year in which the average ticket price reached $7.00.
(b) Verify your result from part (a) algebraically.
(c) Use the model to predict the average ticket price at movie theaters in 2025. Is this prediction reasonable? How does this value compare with the ticket price where you live?