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Problem F-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

F.

Suppose P0 = 96, K = 130, and r = - 0.12. Compute the population size when t = 2, t = 5, t = 10, and t = 100 days. What do you suggest happens to the population size as t → ∞ ? Use the logistic equation above to find your answer.

Tutorial
Using the parameter values given in the problem, we write our model as,


P(t) = 96*130/96+(130-96)*e^-(-0.12)t = 12480/96 + 34 * e^0.12t


Computing the population size at the specified times,

P(2) = 12480/96 + 34 * e^(0.12)*(2) = approx 89.6, P(5) = 12480/96 + 34 * e^(0.12)*(5) = approx 79.0, P(10) = 12480/96 + 34 * e^(0.12)*(10) = approx 59.7, P(100) = 12480/96 + 34 * e^(0.12)*(100) = approx 0.00, width=

We conclude that the population size decreases to extinction as t → ∞. This behavior occurs because r is negative (the death rate is greater than the birth rate).

 

 
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