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Question 3 The logistic model for population growth developed by P.F. Verhulst, is given by - = ap – bp², p(0) = Po > 0 dt where p = p(t) is the population at time t and a, b are positive constants. ap, bp, + (a -bp.)е a and explain why p, # 0,- . b. (a) Show that p(t):

Question 3 The logistic model for population growth developed by P.F. Verhulst, is given by - = ap – bp², p(0) = Po > 0 dt where p = p(t) is the population at time t and a, b are positive constants. ap, bp, + (a -bp.)е a and explain why p, # 0,- . b. (a) Show that p(t):

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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Question 3 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. a (a) Show that p(t) = ap. and explain why Po # 0,- -at bp, + (a – bp,)eat
Transcribed Image Text:Question 3 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. a (a) Show that p(t) = ap. and explain why Po # 0,- -at bp, + (a – bp,)eat
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