01 P 70 2 Phase Portrait 18 a The solution follows the logistic growth solution

# 01 p 70 2 phase portrait 18 a the solution follows

• 14

This preview shows page 13 - 14 out of 14 pages.

01( P - 70) 2 ) Phase Portrait 18. a. The solution follows the logistic growth solution seen in 1. d. The solution is F ( t ) = 10 , 000 50 + 150 e - 0 . 4 t . b. This is a standard logistic growth model, so the equilibria are F e = 0 and 200 (thousand). Below is a sketch of the function with the phase portrait. The equilibrium F e = 0 is unstable, while the carrying capacity, F e = 200 (thousand), is a stable equilibrium. -50 0 50 100 150 200 250 -15 -10 -5 0 5 10 15 20 25 > > > > < < F 0 . 4 F ( 1 - F 200 ) Phase Portrait -50 0 50 100 150 200 250 -30 -25 -20 -15 -10 -5 0 5 10 < > > < < < F 0 . 4 F ( 1 - F 200 ) - 15 Phase Portrait Problem 18. b Problem 18. c c. With harvesting, the right hand side of the differential equation is written 0 . 4 F 1 - F 200 - 15 = - 0 . 002 F 2 + 0 . 4 F - 15 = - 0 . 002( F - 50)( F - 150) . It follows that the equilibria are F e = 50 and 150 (thousand). Above is a sketch of the function with the phase portrait. The equilibrium F e = 50 (thousand) is the critical number of fish needed

Subscribe to view the full document.

to avoid extinction and this equilibrium is unstable. The carrying capacity, F e = 150 (thousand), is a stable equilibrium.
• Fall '08
• staff

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask You can ask ( soon) You can ask (will expire )
Answers in as fast as 15 minutes