4. Consider a lake of constant volume 12200 km, which at time I contains an amount y(t) tons of pollutant evenly distributed throughout the lake with a concentration y(1) tons/km. 12200 Assume that fresh water enters the lake at a rate of 67.1 km/yr, and that water leaves the lake at the same rate. Suppose that pollutants are added directly to the lake at a constant rate of 550 tons/yr. Among the many simplifying assumptions that must be made to model such a complicated real-world process is that the pollutants coming into the lake are instantaneously evenly distributed throughout the lake. A. Write a differential equation for y(t). B. Solve the differential equation for initial condition y(0) = 200000 to get an expression for y(t). Use your solution y(t) to describe in practical terms what happens to the amount of pollutants in the lake as goes from 0 to infinity.