Chapter 8.2, Problem 67E

Seasonal business cycle. Suppose that profits on the sale of swimming suits over a 2-year period are given approximately by

     $P\left(t\right)=5-5\cos \frac{\pi t}{26}0\le t\le 104$

where P is profit (in hundreds of dollars) for a week of sales t weeks after January 1. The graph of the profit function is shown in the figure.

(A)    Find the exact values of P(13), P(26), P(39), and P(52) without using a calculator.

(B)    Use a calculator to find P(30) and P(100). Interpret the results.

(C)    Use a graphing calculator to confirm the graph shown here for y = P(t).