Question: An aquarium pool has volume 2 · 106 liters. The pool initially contains pure fresh water. At t = 0 minutes, water containing 10 grams/liter of salt is poured into the pool at a rate of 60 liters/minute. The salt water instantly mixes with the fresh water, and the excess mixture is drained out of the pool at the same rate (60 liters/minute).
(a) Write a differential equation for S(t), the mass of salt in the pool at time t.
(b) Solve the differential equation to find S(t).
(c) What happens to S(t) as t → ∞?