Suppose a Population Growth Is Modeled by the Logistic Equation $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$

question 10

Multiple Choice

Suppose a population growth is modeled by the logistic equation $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$ with P(0) = 10. Find the formula for the population after t years.

• A) \(P ( t ) = \frac { 100 } { 1 + 9 e ^ { - 0.01 t } }\)
• B) \(P ( t ) = \frac { 100 } { 1 + 10 e ^ { - 0.01 t } }\)
• C) \(P ( t ) = \frac { 100 } { 1 + e ^ { - 0.01 t } }\)
• D) \(P ( t ) = \frac { 10 } { 1 + 9 e ^ { - 0.01 t } }\)
• E) \(P ( t ) = \frac { 10 } { 1 + e ^ { - 0.01 t } }\)
• F) \(P ( t ) = \frac { 100 } { 1 - 9 e ^ { - 0.01 t } }\)
• G) \(P ( t ) = \frac { 100 } { 1 + 9 e ^ { - 0.1 t } }\)
• H) \(P ( t ) = 100 e ^ { 0.01 t }\)

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Definitions:

Indirect Labor

Labor costs associated with employees who do not work directly on the production of goods or services but support the production environment, such as maintenance staff and supervisors.

Decision-Making

The process of selecting the best course of action from multiple alternatives to achieve a desired goal or solve a problem.

Management Function

Activities and responsibilities undertaken by managers to plan, organize, lead, and control resources to achieve specific organizational goals.

Controlling

The process of monitoring, comparing, and correcting plan performance to ensure that organizational goals are achieved efficiently and effectively.