The inflow to a small reservoir during a storm may be described by the equation Q=1000(1-e ^-kt )

where Q= flow in cfs

k=runoff rate=1.0 per hour

t= time in hours

The outflow through the dam gates is held constant at 800cfs. the initial volume of the reservoir is 10*10^6 cubic feet. Write the differential equation describing the rate of change in reservoir volume with time. Plot the volume of the reservoir versus time during the first 8hours of the storm. At what time does the minimum volume occur? Does a maximum volume occur?