A tank contains 150 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

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Answer:The number A(t) of grams of salt in the tank at time t is

Explanation:Knowing

First we have to find the Rin and Rout

Rin = (concentration of the salt inflow) * (input rate of brine)

Rin = 1 g/L * 3 L/min = 3 g/L

Rout = (concentration of the salt outflow) * (output rate of brine)

Rout = () * (3 L/min) =

Substituting this results

= 3 – –>

Thus, integration factors is

A(t) = 4

Applying the initial conditions

A(0) = 40

c = 150 – 40 = 110

Now, substitute this result in the solution to get