where r is the population growth/decay rate, and K is the population carrying capacity. Consider the values Po = 50, K = 300, r = 0.1. a. Find the equilibrium population(s). b. Solve the IVP. Then, compute P(16). Remark. Solve the DE as a Bernoulli DE. c. Find the limiting population and give a physical interpretation to your finding. d. Sketch the population curve versus time showing your findings in Parts b and c.
where r is the population growth/decay rate, and K is the population carrying capacity. Consider the values Po = 50, K = 300, r = 0.1. a. Find the equilibrium population(s). b. Solve the IVP. Then, compute P(16). Remark. Solve the DE as a Bernoulli DE. c. Find the limiting population and give a physical interpretation to your finding. d. Sketch the population curve versus time showing your findings in Parts b and c.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Solve part d please
Transcribed Image Text:2. (Population Logistic Model) Let P(t) represent the population of a certain species at time t.
The following IVP describes the growth/decay of the population
dP = TP (1-P). P(0) = Po
dt
K
where r is the population growth/decay rate, and K is the population carrying capacity.
Consider the values Po = 50, K = 300, r = 0.1.
a. Find the equilibrium population(s).
b. Solve the IVP. Then, compute P(16). Remark. Solve the DE as a Bernoulli DE.
c. Find the limiting population and give a physical interpretation to your finding.
d. Sketch the population curve versus time showing your findings in Parts b and c.
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