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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

Problem D-Predict how a population will change over time

Using this model, answer the following question.

D.

Suppose r = 0.16, P0 = 254, and K = 125. Compute the population size when

= 2, = 5, t = 10, and = 100 days.

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

A.
P(t) → 0 as t → ∞.
B.
P(t) → 254 as t → ∞.
C.
P(t) → – ∞ as t → ∞.
D.
P(t) → 125 as t → ∞.
E.
P(t) → ∞ as t → ∞.

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The Biology Project > Biomath > Applications > Logistic Population Model


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The University of Arizona

December 2005
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