Question

A shallow reservoir has a one-square-kilometer water surface and an average water depth of 2 meters. Initially it is filled with fresh water, but at time t=0 water contaminated with a liquid pollutant begins flowing into the reservoir at the rate of 200 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)=20 liters per cubic meter (L/m^3). Verify that the graph of x(t) resembles the steadily rising curve shown here, which approaches asymptotically the graph of the equilibrium solution x(t)=40 that corresponds to the reservoir's long-term pollutant content. How long does it take the pollutant concentration in the reservoir to reach (10 L/m^3)?

Answer 1