Question

A shallow reservoir has a​ one-square-kilometer water surface and an average water depth of 4 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 500 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)=2020 liters per cubic meter ​(L/m cubedm3​). 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) ≡ 80 that corresponds to the​ reservoir's long-term pollutant content. How long does it take the pollutant concentration in the reservoir to reach 1616 ​L/m cubedm3​?

Answer 1