Consider a large vat containing sugar water that is to be made into soft drinks (see figure below). A B Suppose: The vat contains 200 gallons of liquid, which never changes. Sugar water with a concentration of 10 tablespoons/gallon flows through pipe A into the vat at the rate of 8 gallons/minute. Sugar water with a concentration of 8 tablespoons/gallon flows through pipe B into the vat at the rate of 32 gallons/minute. The liquid in the vat is kept well-mixed. Sugar water leaves the vat through pipe C at the rate of 40 gallons/minute. Before the process starts the vat contains 36 tablespoons of sugar. Let S(t) represent the number of tablespoons of sugar in the vat at time t, where t is given in minutes. (a) Write the DE model for the rate of change of sugar with respect to time in the vat: ds dt (b) Find an expression for S(t). S(t) =