The Population of a Town Increases at a Rate Proportional $P ( t )$

question 34

Multiple Choice

The population of a town increases at a rate proportional to its population. Its initial population is 5000. The correct initial value problem for the population, $P ( t )$ , as a function of time, t, is

• A) \(\frac { d P } { d t } = k P , P ( 0 ) = 5000\)
• B) \(\frac { d P } { d t } = k P ^ { 2 } , P ( 0 ) = 500\)
• C) \(\frac { d P } { d t } = k P , P ( 0 ) = 500\)
• D) \(\frac { d P } { d t } = k P ( 1 - P ) , P ( 0 ) = 5000\)
• E) \(\frac { d P } { d t } = k P ^ { 2 } , P ( 0 ) = 5000\)

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Definitions:

Brand Equity

The value premium that a company realizes from a product with a recognizable name as compared to its generic equivalent.

Consumers

Individuals or groups who purchase goods or services for personal use and not for manufacturing or resale.

Promise

A declaration or assurance that one will do something or that a particular thing will happen.

Value

The importance, worth, or usefulness of something, often considered in terms of how much something is worth to someone.