Question

The population of elk in a region of a national forest was 290 in 1980 and 370 in 1990. Experienced forest rangers estimate that the carrying capacity of the elk for the size and location of the region under consideration is 800. They want to estimate the population of elk in 2010. What is their estimate? Use the equation for the logistic growth model.

Answer 1

Solution

from the problem logistic growth model differential equation is:

Where P is the population at a time t, k is a constant of proportionality and K is the carrying capacity.

So, at t=0 (1980), P=290=P_o

at t=10 (1990), P=370

K=800.

And the differential equation has a solution of this form:

    and

Calculating A:

Meaning that:

and to calculate k then we use t=10 and P(10)=370

And finally the population at a time t is calculated by:

The year 2010 will be t=30 then the population for the year 2010 will be: