Consider the logistic equation dP dt -KP(1-B) =-kP where k> 0 and B> 0 are constants. (a) Find and classify equilibrium solutions and draw a phase line. (b) Use your work from part (a) to sketch the family of solutions corresponding to this differential equation. (c) If P(t) represents a population that is governed by the reverse logistic equation, use your work in part (b) to interpret the behavior of P(t) and explain the possible fates of such a population. (d) Use your results from part (c) to determine the arbitrary constant if P(0) = Po. Is it possible to evaluate the lim P(t)? If so, evaluate the limit, if not, explain why. t-∞
Consider the logistic equation dP dt -KP(1-B) =-kP where k> 0 and B> 0 are constants. (a) Find and classify equilibrium solutions and draw a phase line. (b) Use your work from part (a) to sketch the family of solutions corresponding to this differential equation. (c) If P(t) represents a population that is governed by the reverse logistic equation, use your work in part (b) to interpret the behavior of P(t) and explain the possible fates of such a population. (d) Use your results from part (c) to determine the arbitrary constant if P(0) = Po. Is it possible to evaluate the lim P(t)? If so, evaluate the limit, if not, explain why. 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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Transcribed Image Text:Consider the logistic equation
dP
dt
=
-KP(1-B)
where k> 0 and B> 0 are constants.
(a) Find and classify equilibrium solutions and draw a phase line.
(b) Use your work from part (a) to sketch the family of solutions corresponding to this differential equation.
(c) If P(t) represents a population that is governed by the reverse logistic equation, use your work in part (b) to
interpret the behavior of P(t) and explain the possible fates of such a population.
(d) Use your results from part (c) to determine the arbitrary constant if P(0) = Po. Is it possible to evaluate the
lim P(t)? If so, evaluate the limit, if not, explain why.
t-∞0
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