Chapter 6.2, Problem 12E

Reminder Round all answers to two decimal places unless otherwise indicated.

Water in a Tank Water is leaking out of a tank. The amount of water in the tank $t$ minutes after it springs a leak is given by $W\left(t\right)$ gallons.

a. Explain what $\frac{dW}{dt}$ means in practical terms.

b. As water leaks out of the tank, is $\frac{dW}{dt}$ positive or negative?

c. For the first 10 minutes, water is leaking from the tank at a rate of 5 gallons per minute. What do you conclude about the nature of the function $W$ during this period?

d. After about 10 minutes, the hole in the tank suddenly gets larger, and water begins to leak out of the tank at 12 gallons per minute.

i. Make a graph of $W$ versus $t$. Be sure to incorporate linearity where it is appropriate.

ii. Make a graph of $\frac{dW}{dt}$ versus $t$.