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

question 158

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:

Negative Stroke

A form of feedback or communication that conveys disapproval, criticism, or a negative assessment towards someone's actions or behaviors.

Supervisor

An individual in a position of authority responsible for overseeing and guiding employees' or team members' work within an organization.

Hierarchy of Needs

A theory in psychology proposed by Abraham Maslow that outlines a five-tier model of human needs, from basic (physiological) to higher (self-actualization) needs.

Physiological Needs

Basic physical requirements for human survival, such as food, water, shelter, and sleep, posited as the foundation of Maslow's hierarchy of needs.