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The logistic model for population growth developed by P.F. Verhulst, is given by dp = ap – bp, dt p(0) = P, > 0 where p = p(t) is the population at time t and a, b are positive constants. Show that p(t) = ар. and explain why Po # 0, (a) bp, + (a – bp, )e at ª . (b) Find the limit of p(1) when (i) (ii) t →-00.

The logistic model for population growth developed by P.F. Verhulst, is given by dp = ap – bp, dt p(0) = P, > 0 where p = p(t) is the population at time t and a, b are positive constants. Show that p(t) = ар. and explain why Po # 0, (a) bp, + (a – bp, )e at ª . (b) Find the limit of p(1) when (i) (ii) t →-00.

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 logistic model for population growth developed by P.F. Verhulst, is given by dp = ap – bp, dt p(0) = Po > 0 where p = p(t) is the population at time t and a, b are positive constants. apo Show that p(t) = bp, +(a – bp,)e™ (a) and explain why Po # 0, (b) Find the limit of p(t) when (i) (ii) t → -00.
Transcribed Image Text:The logistic model for population growth developed by P.F. Verhulst, is given by dp = ap – bp, dt p(0) = Po > 0 where p = p(t) is the population at time t and a, b are positive constants. apo Show that p(t) = bp, +(a – bp,)e™ (a) and explain why Po # 0, (b) Find the limit of p(t) when (i) (ii) t → -00.
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