Martha Stewart is mixing up a big batch of eggnog for the holidays. Suppose she has a big mixing vat containing 100 gallons of egg yolks. At time t = 0, her assistant starts pouring a milk and sugar mixture containing 1/2 lb of sugar per gallon into the vat at a rate of 4 gallons per minute. At the same time, mixed eggnog starts leaving the vat a rate of 4 gallons per minute. Let S(t) be the amount of sugar (measured in pounds) in the vat at time t, where t is measured in minutes. Required:
a. At time t, how many gallons of eggnog are in the vat?
b. At time t, what is the rate at which sugar is entering the vat?