1. Suppose that a population grows according to the logistic equation dP dt where t is...
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1. Suppose that a population grows according to the logistic equation dP dt where t is measured in weeks. 0.05P-0.0005P² (a) (2 marks) What are the equilibrium solutions for the differential equation? (b) (1 mark) For which value of P is the slope largest? (c) (2 marks) Use MATLAB to sketch the slope field for this equation for the differential equation. Submit your code and a picture of the slope field. Which solutions are increasing? Which solutions are decreasing? (d) (2 marks) On the slope field in (c), sketch (by hand) the solutions for initial populations of 20 and 120. Do the solution curves have inflection points? At what population level(s) do the inflection points occur? (e) (3 marks) Solve the differential equation. 1. Suppose that a population grows according to the logistic equation dP dt where t is measured in weeks. 0.05P-0.0005P² (a) (2 marks) What are the equilibrium solutions for the differential equation? (b) (1 mark) For which value of P is the slope largest? (c) (2 marks) Use MATLAB to sketch the slope field for this equation for the differential equation. Submit your code and a picture of the slope field. Which solutions are increasing? Which solutions are decreasing? (d) (2 marks) On the slope field in (c), sketch (by hand) the solutions for initial populations of 20 and 120. Do the solution curves have inflection points? At what population level(s) do the inflection points occur? (e) (3 marks) Solve the differential equation.
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dP dt 005P00005P 005P00005P 0 005P1 001P 0 If either 005 P 0 or 1001P 0 That is 0 by us... View the full answer
Related Book For
Auditing and Assurance Services
ISBN: 978-0077862343
6th edition
Authors: Timothy Louwers, Robert Ramsay, David Sinason, Jerry Straws
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