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 a rate of 14 gals/min. (a) Write a differential equation and the initial condition for A, the number of pounds of salt in the tank, at time t. Show your construction step-by-step with verbal explanations. Include the discovery of • how many pounds of salt is pumped in per minute. • the volume of solution in the tank at time t, the concentration (pound per gallon) of salt in the tank at time t expressed in terms of both A and t, how much salt is pumped out per minute, also expressed in terms of A and t, (b) Solve the differential equation to find A(t), the amount of salt in the tank at time t.

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