The water level in a municipal reservoir has been decreasing steadily during a dry spell, and there is a concern that the drought could continue for another 60 days. The local water company estimates that the consumption rate in the city is approximately 107 L/day. The state conservation service estimates that rainfall and stream drainage into the reservoir coupled with evaporation from the reservoir should yield a net water input rate of 106 exp (-t/100) L/day, where t is the time in days from the beginning of the drought, at which time the reservoir contained an estimated 109 liters of water. Integrate the balance to calculate the reservoir volume at the end of the 60 days of continued drought.

We now separate variables and integrate the differential balance equation from t=0 to t= 60 days.