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 Assume that the bills are put into circulation at a constant rate and continuously, and that they are withdrawn from circulation without regard to their condition, in a random manner.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) How many new bills will be in circulation at any time?

(b) 21 years later, how many old bills will still be in circulation?