Acertain small country has $10 billion in paper currency in circulation. each day $50 million of the money in circulation enters the country’s banks, and another $50 million leaves the banks and enters circulation. the government decides to introduce new currency by having the banks replace the old bills with the new ones whenever old currency comes into the banks. let x = x(t) denote the amount of new currency in circulation at time t, with x(0) = 0. assume that the proportion of new money entering the banks each day is the same as the proportion of new money in circulation. how long would you estimate it to take for the new bills to account for 90% of the currency in circulation?