Concept explainers
a.
To formulate: A mathematical model in the form of an initial-value problem that represents the flow of the new currency into circulation.
a.
Answer to Problem 44E
Explanation of Solution
Given information:
Total paper currency is $10 billion. Each day
Concept used :
At first there is no new currency. So all the currency comes to the bank is replaced by new one. But as the time passes (in fact, from second day) the currency the currency come into the bank will be mixed i.e. old one and new one. So, bank only replace old one.
Calculation:
Let,
On the day
Out of which new currency will be
So, on that day bank will replace
So, we can write,
b.
To solve: Initial-value problem found in part (a)
b.
Answer to Problem 44E
Explanation of Solution
Given information:
Formula used:
Calculation:
Integrating both sides,
Now,
Therefore,
So,
c.
To calculate: How long it will take for new bills to account for
c.
Answer to Problem 44E
It will take about
Explanation of Solution
Given information:
Formula used :
Here,
Calculation:
Total paper currency
So,
Therefore, it will take about
Chapter 7 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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