Suppose That a Population Grows According to a Logistic Model $k = 0.05$

question 119

Multiple Choice

Suppose that a population grows according to a logistic model with carrying capacity 2,000 and $k = 0.05$ per year. Choose the logistic differential equation for these data.

• A) \(\frac { d P ( t ) } { d t } = P \left( 1 + \frac { p } { 2,000 } \right)\)
• B) \(\frac { d P ( t ) } { d t } = 0.05 P \left( 1 + \frac { p } { 5 } \right)\)
• C) \(\frac { d P ( t ) } { d t } = 2,000 P \left( 1 + \frac { p } { 0.05 } \right)\)
• D) \(\frac { d P ( t ) } { d t } = 0.05 P \left( 1 + \frac { p } { 2,000 } \right)\)
• E) \(\frac { d P ( t ) } { d t } = 0.05 P \left( 1 - \frac { p } { 2,000 } \right)\)

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Definitions:

Nonlinear Optimization Model

A type of optimization model where the objective function or any of the constraints are nonlinear functions.

Constant Times

Specific, unchanging durations that are relevant in certain procedural or computational contexts.

Forecast Statistic

The estimation of future values based on historical data and analysis methodologies.

Upper Bound

In mathematics, the upper limit of a set of values. It is the largest value that would not be exceeded by any element of the set.