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:

Stem Apical Meristem

A region at the tip of a plant stem where cells are undifferentiated and capable of division, contributing to the lengthwise growth of the plant.

Lateral Meristems

Plant tissue responsible for growth in thickness or girth in a maturing plant, found in the cambium and producing cells that differentiate into various tissues.

Leaf Primordia

Embryonic tissues at the tips of plant shoots that develop into leaves.

Meristematic Cells

Undifferentiated cells in plants that are capable of division and contribute to plant growth, found in regions like the tips of roots and shoots.