Chapter 8.3, Problem 52E

Average Daylight Hours The number of hours of daylight per day in Washington, D.C., $t$ weeks after the beginning of the year is

$f(t)=12.18+2.725\sin \left[\frac{2\pi }{52}\left(t-12\right)\right]$.

The graph of this function is sketched in Fig. 13.

How many hours of daylight are there after $42$ weeks?

After $32$ weeks, how fast is the number of hours of daylight decreasing?

When is there $14$ hours of daylight per day?

When is the number of hours of daylight increasing at the rate of $15$ minute per week?

When are the days longest? Shortest?

When is the number of hours of daylight increasing fastest? Decreasing fastest?