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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In this question, where did e^(1/20) come from?
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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