A Population Is Modeled by the Differential Equation $\frac { d P } { d t } = 0.4 P \left( 1 - \frac { P } { 250 } \right)$

question 137

Essay

A population is modeled by the differential equation $\frac { d P } { d t } = 0.4 P \left( 1 - \frac { P } { 250 } \right)$ where $P ( t )$ is the population at time $t$ .(a) What are the equilibrium solutions?
(b) For what values of $P$ is the population increasing?
(c) For what values of $P$ is the population decreasing?
(d) Use the information from above to sketch the direction field for the given differential equation.

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Definitions:

Fixed Costs

Expenses that do not change with the level of production or sales, such as rent, salaries, and insurance premiums.

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Documents that compare actual business results to planned or budgeted figures to evaluate performance.

Flexible Budget

A budget that adjusts or flexes with changes in volume or activity levels, used to compare actual performance against what should have occurred at the actual level of activity.

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A fixed budget that does not change with the level of activity or production volume, often used for planning purposes.