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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

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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
Problem 44PPS
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●●● 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 ·currency passes through the banks. So we have: dN 1/10 (100-N) = both linear and separable dt 20 dN // N = 5 Want t when N(E)= 90 dt - fot •Fot m(t)= e 90= 100 - 100e M - t žot d # (e tot N) = Se tut =e е e tot N е = 100e Fot 20 Info N(t) = 100 + се N(0) = 0 => (= -100 N(t) = 100 - 100e fo = + с - stat - Fot t= = 201~10 ~46 days akázaným ministara ZAKONANİDENİZİN
Transcribed Image Text:●●● 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 ·currency passes through the banks. So we have: dN 1/10 (100-N) = both linear and separable dt 20 dN // N = 5 Want t when N(E)= 90 dt - fot •Fot m(t)= e 90= 100 - 100e M - t žot d # (e tot N) = Se tut =e е e tot N е = 100e Fot 20 Info N(t) = 100 + се N(0) = 0 => (= -100 N(t) = 100 - 100e fo = + с - stat - Fot t= = 201~10 ~46 days akázaným ministara ZAKONANİDENİZİN
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