A logistic initial value problem is given by dP — kP(М — Р), P(0) — Ро. dt M Po i. Show that P(t) Ро + (М — Р)е-kMt" ii. Describe the behaviour of P(t) as t → o and 0 < Po < M..

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
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A logistic initial value problem is given by
dP
— kP(М — Р), P(0) — Ро.
dt
M Po
i. Show that P(t)
Ро + (М — Р)е-kMt"
ii. Describe the behaviour of P(t) as t → o and 0 < Po < M..
Transcribed Image Text:A logistic initial value problem is given by dP — kP(М — Р), P(0) — Ро. dt M Po i. Show that P(t) Ро + (М — Р)е-kMt" ii. Describe the behaviour of P(t) as t → o and 0 < Po < M..
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