A swimming pool holds 10,000 gallons of water. It is being filled at a rate of 400 gallons per hour.

Part A: Write an equation for the function modeling the number of gallons of water, y, in the pool x hours after it began to be filled.

Part B: What is the rate of change of this function?

We are told that dV/dt=400 gal/hr so that is the rate asked for in part B.

So to find the function for V (t) you need to integrate dV/dt ...

V (t) = ⌠400 dt

V (t) = 400t + C, where C is the initial volume which is not specified so we can assume that C=0, or in terms of y and x for the labels ...

y (x) = 400x