{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

logististModelWS

# logististModelWS - Math 227 Section 4 and 5 Worksheet on...

This preview shows pages 1–2. Sign up to view the full content.

Math 227 Section 4 and 5 Worksheet on the Logistic Growth Model Due March 21 Name Instructions. Write up your solutions using brief but complete English and algebraic sentences and appro- priate punctuation. Poorly written work will not be graded. Let t denote time and P ( t ) the number of individuals in a population at time t: The logistic growth model is based on the following di/erential equation: dP dt = kP ° (1 ± P B ) where k and B are positive constants. It is assumed that initially, 0 < P < B: When P is small, we have dP dt ² kP; so the constant k can be viewed as the instrinsic growth rate of the population. When P gets large (but less than B ) , the factor (1 ± P=B ) diminishes the rate of growth. As you will see, P will never reach or exceed B: The constant B is called the carrying capacity . 1. Separate variables and solve the di/erential equation. Show that its general solution satis°es the equation P B ± P = Ce kt : where C is a constant.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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