Water pumped into and drained from a tank

Name: ______________________ Date: ____________ Water pumped into and drained from a tank (9 points)

Graph

Water is pumped into a tank at a rate modeled by

E(t)

= 50 + 30\sin\left(\frac{t^2}{40}\right)

liters per hour, and water drains from the tank at a rate modeled by

D(t) = 15 + 9t

liters per hour, for

0 \le t \le 10

hours. At time

t = 0

the tank holds 200 liters. The graph shows both rates.

(a) How many liters of water are pumped into the tank from $t = 0$ to $t = 10$ hours? [2 points]
(b) Is the amount of water in the tank increasing or decreasing at time $t = 6$ hours? Give a reason for your answer. [2 points]
(c) Write an expression involving one or more integrals that gives the amount of water $A(t)$ , in liters, in the tank at time $t$ . [2 points]
(d) Find the absolute maximum amount of water in the tank for $0 \le t \le 10$ . Justify your answer. [3 points]

The question