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(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 P(0) = Po 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. dP dt P(1-K). =rP1 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.

(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 P(0) = Po 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. dP dt P(1-K). =rP1 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.

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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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.
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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