A certain small country has $10 billion in paper currency in circulation, and each day $40 million comes into the countr

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A Certain Small Country Has 10 Billion In Paper Currency In Circulation And Each Day 40 Million Comes Into The Countr 1 (21.86 KiB) Viewed 14 times

A certain small country has $10 billion in paper currency in circulation, and each day $40 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let xx(0) denote the amount of new currency (in billions of dollars) in circulation at time t (in days), with x(0) - 0. (a) Formulate a mathematical model in the form of an initial-value problem that represents the flow of the new currency into circulation dx dr q *(0) - - (b) Solve the initial-value problem found in part (a). *(1) - (c) How long will it take for the new bills to account for 90% of the currency in circulation? (Round your answer to the nearest hundredth of a year) years