Suppose a Population Growth Is Modeled by the Logistic Equation $\frac { d P } { d t } = 0.0001 P ( 1000 - P )$

question 90

Multiple Choice

Suppose a population growth is modeled by the logistic equation $\frac { d P } { d t } = 0.0001 P ( 1000 - P )$ with P(0) = 10. Find the formula for the population after t years.

• A) \(P ( t ) = \frac { 1000 } { 1 + 99 e ^ { - 0.01 t } }\)
• B) \(P ( t ) = \frac { 1000 } { 1 + 10 e ^ { - 0.01 t } }\)
• C) \(P ( t ) = \frac { 1000 } { 1 + e ^ { - 0.01 t } }\)
• D) \(P ( t ) = \frac { 100 } { 1 + 9 e ^ { - 0.01 t } }\)
• E) \(P ( t ) = \frac { 1000 } { 1 + 9 e ^ { - 0.01 t } }\)
• F) \(P ( t ) = \frac { 100 } { 1 - 99 e ^ { - 0.01 t } }\)
• G) \(P ( t ) = \frac { 1000 } { 1 + 99 e ^ { - 0.1 t } }\)
• H) \(P ( t ) = 1000 e ^ { 0.1 t }\)

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