Assume that the population of a species grows according to the model dP — 2(Р— 2) (100 — Р). dt (3.1) Draw the phase line of the system. (3.2) Explain how the population behaves, for the following initial values: (a) P(0) = 1; (b) P (0) = 50; (с) Р () — 150.

Assume that the population of a species grows according to the model dP — 2(Р— 2) (100 — Р). dt (3.1) Draw the phase line of the system. (3.2) Explain how the population behaves, for the following initial values: (a) P(0) = 1; (b) P (0) = 50; (с) Р () — 150.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Assume that the population of a species grows according to the model
dP
— 2(Р — 2) (100 — Р).
dt
(3.1) Draw the phase line of the system.
(3.2) Explain how the population behaves, for the following initial values:
(а) Р (0)
= I;
(b) P (0) = 50;
(с) Р (0) %—D 150.

(3.3) Are there any initial population sizes in this model for which the population grows without
bound? Justify your answer.

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