A tank initially contains w liters of a solution in which is dissolvedA0 grams of chemic...

A tank initially contains w liters of a solution in which is dissolvedA₀ grams of chemical.Asolution containing k g/L of this chemical flows into the tank at a rate of r L/min, and the mixture flows out at the same rate.

(a) Show that the amount of chemical, A(t), in the tank at time t is

(b) Show that as t →∞, the concentration of chemical in the tank approaches k g/L. Is this result reasonable? Explain.