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

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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.
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