Consider a poputation Piti satistying the extinction expiosion equation-ap - bP. where B= aPis the sime rate at which births occur and D= bPis the rate at which deaths occur. If the initial population is PI0) = P, and B, births per month and Dg deaths per month are occurring at time t=0, show that the threshold population is M ap -bP can be rewritten in the form PIM - P) where k -a and M= Since, DbP and Bap, Mcan be rewritten in terms of B. D. and P.
Consider a poputation Piti satistying the extinction expiosion equation-ap - bP. where B= aPis the sime rate at which births occur and D= bPis the rate at which deaths occur. If the initial population is PI0) = P, and B, births per month and Dg deaths per month are occurring at time t=0, show that the threshold population is M ap -bP can be rewritten in the form PIM - P) where k -a and M= Since, DbP and Bap, Mcan be rewritten in terms of B. D. and P.
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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Transcribed Image Text:Consider a population P(t) satisfying the extinction explosion equation = ap - bP. where B= ap is the time rate at which births occur and D = bP is the rate at which deaths occur. If the initial population is P(0) = P, and B births per month and
D,P.
D, deaths per month are occurring at time t=0, show that the threshold population is M=
B.
dP
== ap - bP can be rewritten in the form = kP(M - P) where k= -a and M=-
Since, D= bP and B= aP, M can be rewritten in terms of B. D, and P.
M-0
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