Question: An aquarium pool has \(2 \cdot 10^{6}\) liters. The pool initially contains pure fresh water, At \(t=0\) minutes, water containing 10 grams/liter of salt is poured into 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 (6o liters/minute).

a.) Write a differential equation for \(S(t)\), the mass of salt water in the pool at time \(t\).

b.) Solve the differential equation to find \(S(t)\).

c. What happens to \(S(t)\) as \(t \rightarrow \infty\) ?

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