Unsteady State

The dry season caused the water level in reservoir to be decreasing. The metrologies

announced that the drought for that year would be continued for another $70$ days. They also

estimate that the consumption rate in the city is approximately $107\frac{L}{?}$ day. On the other hand,

they estimate that rainfall and stream drainage into the reservoir including the evaporation

should yield net water input rate of $106$exp$(-\frac{t}{100})\frac{L}{?}$ day, where $t$ is the time in days for the

beginning of the drought. Initial volume of the reservoir at the day one of the dry season is

estimated to be $109$ litre.

Write a balance equation describing the water in the reservoir. Then, integrate the balance to

calculate the reservoir volume at the end of $70$ days of drought.