Question

The rate at which water is entering a reservoir is given for time greater than zero in the graph. A negative rate means that water is leaving the reservoir. On which interval is the volume of water in the reservoir increasing the fastest??

Answer 1

The volume of water in the reservoir is increasing the fastest during the interval where the rate of water inflow is at its maximum.

Step-by-step explanation:

To identify the interval during which the volume of water in the reservoir is increasing the fastest, we need to analyze the graph of the rate at which water is entering or leaving the reservoir. The steepest positive slope on the graph corresponds to the interval with the highest rate of water inflow, indicating the fastest increase in volume.

Let's denote the time intervals as Δt and the corresponding rates as ΔV/Δt, where ΔV is the change in volume. The interval with the highest positive rate (ΔV/Δt > 0) will signify the fastest increase in volume.

It's important to consider the units of the rates, ensuring they match the units of volume per unit time (e.g., cubic meters per second). The interval with the largest positive rate indicates when water is entering the reservoir at the fastest rate, contributing to the highest increase in volume.