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3. Suppose a population P(t) evolves according to the logistics equation = 0.3P-0.001P². dP dt a) Draw a phase line for P. What is Po? b) Suppose P(0) = 100. Solve for P(t). What is P(10)? Hint: the above equation is of the Bernoulli type (§ 2.6).

3. Suppose a population P(t) evolves according to the logistics equation = 0.3P-0.001P². dP dt a) Draw a phase line for P. What is Po? b) Suppose P(0) = 100. Solve for P(t). What is P(10)? Hint: the above equation is of the Bernoulli type (§ 2.6).

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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3. Suppose a population P(t) evolves according to the logistics equation = 0.3P-0.001P². dP dt a) Draw a phase line for P. What is Po? b) Suppose P(0) = 100. Solve for P(t). What is P(10)? Hint: the above equation is of the Bernoulli type (§ 2.6). 4. Suppose a quantity X changes according to the law 0.25X0.01X³. dX dt 4 Identify the equilibrium solutions for X and draw a phase line for X. If X(0) = 3, what is limt X(t)? The phase line should indicate this. 88 =
Transcribed Image Text:3. Suppose a population P(t) evolves according to the logistics equation = 0.3P-0.001P². dP dt a) Draw a phase line for P. What is Po? b) Suppose P(0) = 100. Solve for P(t). What is P(10)? Hint: the above equation is of the Bernoulli type (§ 2.6). 4. Suppose a quantity X changes according to the law 0.25X0.01X³. dX dt 4 Identify the equilibrium solutions for X and draw a phase line for X. If X(0) = 3, what is limt X(t)? The phase line should indicate this. 88 =
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