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The size of a population (in thousands), P(t), at time t is given by the equation dP %3D — Р(Р — 2)(Р - 10) dt

The size of a population (in thousands), P(t), at time t is given by the equation dP %3D — Р(Р — 2)(Р - 10) dt

Advanced Engineering Mathematics
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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The size of a population (in thousands), P(t), at time t is given by the equation dP 3D — Р(P - 2)(Р — 10) dt (a) What are the critical points of the equation? (b) Draw a graph of several trajectories of the equation. Include the graphs of the equilibrium (constant) solutions as well as a few trajectories between each of the equilibrium trajectories. (c) What is the fate (that is, find lim,co P(t)) of a population that is initially 8000? (d) What is the fate of a population that is initially 1000?
Transcribed Image Text:The size of a population (in thousands), P(t), at time t is given by the equation dP 3D — Р(P - 2)(Р — 10) dt (a) What are the critical points of the equation? (b) Draw a graph of several trajectories of the equation. Include the graphs of the equilibrium (constant) solutions as well as a few trajectories between each of the equilibrium trajectories. (c) What is the fate (that is, find lim,co P(t)) of a population that is initially 8000? (d) What is the fate of a population that is initially 1000?
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