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:

Wage Rates

The standard amount of compensation that workers receive in exchange for their labor, often expressed per hour or per unit of work.

Associational Unions

Organizations that represent the interests of a specific group of workers, not based on a particular workplace or employer but rather on shared professions or trades.

Political Pressure

Efforts exerted by individuals, groups, or organizations aiming to influence the decisions or actions of government officials, policy-makers, or any entity in a position of power.

Shareholder Model

A corporate governance framework where the primary focus is on maximizing the value for shareholders.