Problems deal with a shallow reservoir that has a one square kilometer water surface and a...

Problems deal with a shallow reservoir that has a one square kilometer water surface and an average water depth of 2 meters. Initially it is filled with fresh water, bit at time t = 0 water contaminated with a liquid pollutant begins flowing into the reservoir at the rate of 200 thousand cubic meters per month. The well-mixed water in the reservoir flows out at the same rate. Your first task is to find the amount x(t) of pollutant (in millions of liters) in the reservoir after t months.

The incoming water has a pollutant concentration of c(t) = 10 liters per cubic meter (L/m3). Verify that the graph of x(t) resembles the steadily rising curve in Fig., which approaches asymptotically the graph of the equilibrium solution x(t) = 20 that corresponds to the reservoir’s long-term pollutant content. How long does it take the pollutant concentration in the reservoir to reach 5 L/m3?

FIGURE. Graphs of solutions in Problems.