Question

The amount of water W in a reservoir t hours after midnight is given by W(1) where W is measured in millions of gallons. Which of the following statements best describes the meaning of W'(3) = 2.45?

a) There are 2.45 million gallons of water in the reservoir at 3:00 AM.
b) A total of 2.45 million gallons of water flow into the reservoir from midnight to 3:00 AM.
c) The amount of water in the reservoir is increasing at a rate of 2.45 million gallons per hour at 3:00 AM.
d) The amount of water in the reservoir increases by 2.45 million gallons from midnight to 3:00 AM.
e) The amount of water in the reservoir is increasing at a rate of 2.45 million gallons per hour from midnight to 3:00 AM.

Answer 1

W'(3) = 2.45 indicates the rate of change of the water amount, which is increasing at a rate of 2.45 million gallons per hour at 3:00 AM.

Step-by-step explanation:

The statement W'(3) = 2.45 represents the rate of change of the water amount in the reservoir at 3:00 AM, specifically how fast the water volume is increasing or decreasing at that exact hour. In this context, W' refers to the derivative of W with respect to time (t), and W'(3) signifies the derivative evaluated at t = 3 hours. Therefore, option (c) - The amount of water in the reservoir is increasing at a rate of 2.45 million gallons per hour at 3:00 AM - best describes the meaning of W'(3) = 2.45.