An aquarium pool has volume 2 · 106 liters. The pool initially contains pure fresh water. At t...

An aquarium pool has volume 2 · 10⁶ liters. The pool initially contains pure fresh water. At t = 0 minutes, water containing 20 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.

dS

dt

=

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

S(t) =

(c) What happens to S(t) as t → ∞?

S(t) → ____________ grams

Expert Solution

milcah answered 3 years ago

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