Chapter 13.1, Problem 46E

Work the given problems. (See Examples 8 and 10.)

Crowd Size The rate of change of the size of the crowd (in people per hour) at a certain theme park is given by

$P^{\prime }\left(t\right)=2800-400t,$

where $t=0$ corresponds to the opening of the park at 8:00 am.

Find the function $P\left(t\right)$ that gives the size of the crowd t hours after opening.

When is the size of the crowd at a maximum?

What is the size of the maximum crowd?