Final answer:
To compute the time, t, as a function of the volume, v, we can use the information given in the graph. The graph shows the volume in the pool increasing over time, which means that the rate of change of volume with respect to time, ∆v/∆t, is positive.
Step-by-step explanation:
To compute the time, t, as a function of the volume, v, we can use the information given in the graph. The graph shows the volume in the pool increasing over time, which means that the rate of change of volume with respect to time, ∆v/∆t, is positive.
We can find the formula by determining the slope of the graph at any given point. The slope represents the rate of change of volume with respect to time. Therefore, the formula for computing the time as a function of the volume is t = f(v), where f(v) is the inverse of the slope function.
For example, if the slope of the graph at a certain point is 0.5 gallons per minute, then f(v) = 1/0.5 = 2 minutes per gallon. So, for a volume of v gallons, the time can be computed as t = 2v minutes.