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