Referring to the previous problem, suppose that during a working day a gang of counterfeiters put into circulation one million dollars in fake onedollar bills.

Data from in previous problem

From the New York Times Magazine, December 25,1955, we read: "The United States Treasury reported that it costs eight-tenths of a cent to print dollar bills, and that of the billion and a quarter now in circulation, a billion have to be replaced annually." Assume that the bills are put into circulation at a constant rate and continuously, and that they are withdrawn from circulation without regard to their condition, in a random manner. Suppose that a new series of dollar bills is put in circulation at a given instant in place of the original bills.

(a) If not detected, what will be the number in circulation as a function of time?

(b) After 10 years, how many of these bills would still be in circulation?