A 75-gallon tank initially holds 35 gallons of salt water containing 6 pounds of salt. Suppose salt water containing 5 pounds of salt per gallon is pumped into the top of the tank at the rate of 8 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 4 gallons per minute. Let S(t) represent the number of pounds of salt in the vat after t minutes. (A) Write the DE model for the time rate of change of salt in the vat. Also include the initial condition. dS/ dt= S(0)= (B) Solve the initial value problem to find the amount of salt in the vat as a function of time. S(t)=. (C) How much salt is in the tank when the tank is full? pounds.