3. A certain small country has 540 billion in paper circulation and each day its citizens deposit $2 billion into the country's banks. The government decides to introduce new currency with the current ruler's likeness by having the banks replace old bills with new bills whenever old currency comes into the banks. Let ctr} denote the amount ofnew currency at time t, with 1(0) 2 U. a) In terms of 3, what fraction of the money in circulation is new currency? b) In terms of :12. what fraction of the money in circulation is old currency? c} Assume that the fraction of new money in circulation is the same as the fraction of money deposited each day. In terms of 1. how much new money is deposited each day (in billions of dollars)? How much old money? d) Write an initial value problem to model this situation. e} How long until 90% of the money in circulation is new money