A tank contains 200 gallons of water in which 300 grams of salt is dissolved. A brine solution containing 0.4 kilograms of salt per gallon of water is pumped into the tank at the rate of 5 gallons per minute, and the well-stirred mixture is pumped out at the same rate. Let LaTeX: A\left(t\right)A(t)[Math Processing Error] represent the amount of salt (measured in kilograms) in the tank at time LaTeX: t[Math Processing Error].

Explanation:

given amount of salt at time t is A(t)

initial amount of salt =300 gm =0.3kg

=>A(0)=0.3

rate of salt inflow =5*0.4= 2 kg/min

rate of salt out flow =5*A/(200)=A/40

rate of change of salt at time t , dA/dt= rate of salt inflow- ratew of salt outflow

integrating factor

integrating factor

multiply on both sides by  

integrate on both sides

b)

after long period of time means t - > ∞

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