Question

Situation 2
A tank initially contains 100 gal of brine where there is dissolved 20lb of salt. Starting at time t = 0, a
brine containing 3lb of dissolved salt per gallon flows into the tank at the rate of 6gal/min is kept uniform
by stirring and the well-stirred mixture simultaneously flows out of the tank at a slower rate of 3gal/min.
1. How much salt is present at the end of 15 min?
2. How much salt is present after a long time?

Answer 1

Let Q be the amount of sait in the tank and $dt/dQ$

​ be the rate of change of amount in the tank

We get the equation as 

$\space dt/ dQ ​ + 1/20 ​ Q=0$

It is linear equation and the solution of it is $Q=Ce ^{-\frac{t}{20} t} ​$

At t=0 , the value of Q is 20 

$⇒C=20$

Therefore the equation is$\space Q=Ce ^{-\frac{t}{20} t}$