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Logistic Population Model


 

P(t) = P<<sub>0</sub> * K / P<sub>0</sub> + (K-P<<sub>0</sub>) * E^-RT


P
(t) is the population size at time t (measured in days)
P0 is the initial population size
K is the carrying capacity of the environment
r is a constant representing population growth or decay

Using this model, answer the following:

Problem C-Predict how a population will change over time

C.

Let r = 0.34, K = 100, and P0 = 12.
Given these value compute the population size when

= 5, = 10, t = 25, = 100, and t = 1000 days.

What do you notice? What do you suggest happens to the population size as t → ∞ ? Use the logistic equation above to find your answer.

A. P(t) → ∞ as t → ∞.
B. P(t) → 100 as t → ∞.
C. P(t) → 0 as t → ∞.
D. P(t) → 12 as t → ∞.
E. P(t) → – ∞ as t → ∞.

 

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The Biology Project > Biomath > Applications > Logistic Population Model


The Biology Project
Department of Biochemistry and Molecular Biophysics

The University of Arizona

February 2005
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