Chapter 6.3, Problem 11E

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

A Pond Water is running out of the pond through a drainpipe. The amount of water, in gallons, in the pond $t$ minutes after the water began draining is given by a function $G=G\left(t\right)$.

a. Explain the meaning of $\frac{dG}{dt}$ in practical terms.

b. While water is running out of the pond, do you expect $\frac{dG}{dt}$ to be positive or negative?

c. When $t=30$, water is running out of the drainpipe at a rate of $8000$ gallons per minute. What is the value of $\frac{dG}{dt}$?

d. When $t=30$, there are $2,000,000$ gallons of water in the pond. Using the information from part c, estimate the value of $G\left(35\right)$.