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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b3ce981-6a21-4ae0-a003-1780f524a708%2F808ff9ab-ccd5-4a5e-aaf2-b6b66e10514c%2F11eni6_processed.png&w=3840&q=75)
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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