Consider the Differential Equation $$\frac { d P ( t ) } { d t } = 0.4 P \left( 1 - \frac { P } { 900 } \right) - c$$

question 97

Short Answer

Consider the differential equation
$$\frac { d P ( t ) } { d t } = 0.4 P \left( 1 - \frac { P } { 900 } \right) - c$$ as a model for a fish population, where $t$ is measured in weeks and $c$ is a constant. For what values of $c$ does the fish population always die out?

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Definitions:

Net Income

The total profit of a company after deducting all expenses, taxes, and losses, indicating its financial performance over a period.

Total Expenses

The sum of all costs and expenses incurred by a business during a specific period, including operating expenses and cost of goods sold.

Direct Materials

Raw materials that can be directly linked to the production of specific goods or services.

Factory Overhead

Indirect costs associated with manufacturing, such as utilities, maintenance, and management expenses, not directly tied to production volumes.