Question

A. Graph Cubas population and describe what pattern you can see. B. Explain why a logistic model would be a better choice for Cubas population growth than an exponential model. C. Find a logistic function f(t)= L/1+C(e^-bt), that models Cubas population growth. - Assume that .039 is a good value for b. Do not change this value - Graph f(t) = 11,000/1+15(e^-.039t) on top of your points (so starting value L=11,000 and the starting value for C=15) - experiment with values for L and C until you have a good model for the graphed points. Limit yourself to L-values between 11,000 and 15,000 and C-values between 11 and 15

Answer 1

A. We have to graph the data (years in the horizontal axis, population in the vertical axis):

B. The shape of the time series match the logisti model: it has an exponential growth in the first stage and then it flattens.

C. We have a logistic model with b=0.039.

We have to plot the function:

`f\mleft(t\mright)=(11000)/(1+15\cdot e^(-0.039t))`

If we add it to the data plot we get:

This parameters do not fit the actual population. So we have to change L between 11000 and 15000 and C between 11 and 15.

If we change them to C=14 and L=13000, we get:

which is a significant better fit than the original model.