A chemical mixing tank

Calculus Level 4

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

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

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


The answer is 130.4007.

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