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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Artesian Well

A well tapping a confined aquifer, where the water pressure is sufficient to bring the water to the surface without pumping.

Water Table

The level below which the ground is completely saturated with water, marking the boundary between the unsaturated soil and the groundwater.

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The upper surface of the saturated zone in the ground where the soil or rocks are permanently wet, marking the boundary between surface water and groundwater.

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The arrangement of the natural and artificial physical features of an area.