A Certain Small Country Has $\$ 20$ Billion in Paper Currency in Circulation, and Each Day

question 118

Short Answer

A certain small country has $\$ 20$ billion in paper currency in circulation, and each day $\$ 70$ million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with 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 $x ( 0 ) = 0$ . Formulate and solve a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency into circulation (in billions per day).

---

Definitions:

Five-Step Process

A systematic approach to problem-solving or project management that involves five distinct stages or steps.

Uncertain Environments

Provide no information to predict expected results for decision-making alternatives.

Information Sufficient

Having enough data or facts to make informed decisions or reach conclusions.

Programmed Decision

A decision made in response to a recurring problem that involves a procedure or rule for its resolution.