A chemical mixing tank

Calculus Level pending



At time \(t = 0\),a tank contains \(Q(0)\) lb of salt dissolved in 100 gallons of water.Assume that water containing \(\frac{1}{4}\) lb of salt/gal is entering the tank at the rate of \(r\) gallon/min and that the well-stirred mixture is draining from the tank at the same rate.

Let \(Q(t)\) denote the amount of salt in the tank at any time \(t\) and \(Q(L)\) denote the amount of salt present after a very long time(infinitely long).

If \(r=3\) and \(Q(0) = 2*Q(L)\),find the time T (in minutes) after which the salt level is within \(2\)% of \(Q(L)\).


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