A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt per gallon is pumped into the tank at a rate of 7 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds of salt in the tank at time t.

Therefore

Step-by-step explanation:

Given that, a large tank contains 700 gallons of pure water.

At a time t , A(t)is the amount of salt in the tank .

The differential equation of rate of change of salt is

First we find and

=(concentration of salt ).(input rate of brine)

     =(3 lb/gal).(7 gal/ min )

     =21 lb/min

Since the rate of solution which is pumped out is same rate of pumped in..

= (the concentration of salt in the tank).(output rate)

      lb/min

    lb/min

Therefore,

 ....(1)

Here and Q = 21

The integrating factor of the differential equation is

=

Multiply the integrating factor the both sides of ODE of (1)

Integrating bot sides

 [c is an arbitrary constant]

At the initial time, the tank contains 700 gallons of pure water.

It means A(0)=0

Putting A=0 ,t=0

Therefore