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..

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 44E
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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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