Consider a tank of constant volume V and containing at time t an amount Q(t) of pollutant, evenly distributed throughout the lake with a concentration c(t), where c(t)-Q(t)/V. Assume that water containing the concentration k of pollutant enters the lake at a rate r, and that water leaves the lake at the same rate.

A) If at time t=0 the concentration of pollutant is C ₀ , find an expression for the concentration c(t) at any time. What is the limiting concentration as t goes to ∞.

B) IF the addition of pollutants to the lake is terminated (k=0 for t>0), determine the time interval t that must elapse before the concentration of pollutants is reduced to 50% of its original value.