Chapter 12, Problem 39RE

Refer to Exercise 38. Determine the average occupancy rate of the hotel over a 1-year period from June 1 through May 31 of the following year.

38. HOTEL OCCUPANCY RATE The occupancy rate (in percent) of a large hotel in Maui in month t is described by the function

$R\left(t\right)=60+37{\sin }^2\left(\frac{\pi t}{12}\right)\left(0\le t\le 12\right)$

where t = 0 corresponds to the beginning of June. When is the occupancy rate highest? When is the occupancy rate increasing most rapidly?