Chapter 6.1, Problem 63E

Filling a reservoir A reservoir with a capacity of 2500 m³ is filled with a single inflow pipe. The reservoir is empty when the inflow pipe is opened at t = 0. Letting Q(t) be the amount of water in the reservoir at time t, the flow rate of water into the reservoir (in m³/hr) oscillates on a 24-hr cycle (see figure) and is given by

$Q^{\prime }(t)=20\left(1+\cos \frac{\pi t}{12}\right).$

1. a. How much water flows into the reservoir in the first 2 hr?
2. b. Find and graph the function that gives the amount of water in the reservoir over the interval [0, t], where t ≥ 0.
3. c. When is the reservoir full?