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Problem D-Predict how a population will change over time

 

Tutorial to help you solve this problem.


 

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

D.

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

t = 2, t = 5, t = 10, and t = 100 days.

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

Tutorial

Using the parameters given in the problem, we write our model as,


P(t) = 254 * 125/254 + (125 - 254) * e^-0.16*t = 31750/1254 - 129 * e^-0.16*t


Computing the population size at the specified times,


P(2) = around 198.0, P(5) = around162.0, P(10) = about139.3, P(100) = around125

We conclude that the population size decreases and approaches 125 individuals (the carrying capacity).

 
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