Q7 A country has 100 billion dollars of currency in circulation, in paper bill form. Money passes through the banks at a continuous rate of 5 billion dollars per day. Suppose the government decides to introduce new paper bills, by replacing all the old bills that pass through the banks with new bills. After how many days will 90% of the currency in circulation be new bills? Let N/t) be the amount of new bills in circulation (in billions) The rate at which N(+) changes is exactly the rate at which old ·currency passes through the banks. So we have : dN 1/0 (100-N) = both linear and separable dt + N = = S Want t when N(E) = 90 - fot 90 100 100e (en) = Se tot ó é e tot N = 100e sot + t = - 20 Info N(E)= 100+ Ce (= -100 100 - 100e. dN dt m(t)= e sot N(0) = 0 N(t) = с - Fot - ot = ~46 days 201n 10

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