A tank contains 350 liters of fluid in which 50 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the number A(t).)

Explanation:

The volume of fluid in the tank =350 liters

Initial Amount of Salt, A(0)=50 grams

Amount of Salt in the Tank

Pure water is then pumped into the tank at a rate of 5 L/min. Therefore:

=(concentration of salt in inflow)(input rate of brine)

=(concentration of salt in outflow)(output rate of brine)

Therefore:

We then solve the resulting differential equation by separation of variables.

Taking the integral of both sides

Recall that when t=0, A(0)=50 grams (our initial condition)

Therefore, the number of grams of salt in the tank at time t is:

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