Only Do 5

Problem 5: (4 pts) Based on your simulations above, what can you conclude about the success of this conservation effort to save black-footed ferrets? Black-footed ferrets Let Pn be the population count of a group of endangered black-footed ferrets in the wild, also known as a "business" of ferrets. Their population is surveyed every year (N) and thought to be modelled by the equation Pn+1 = (1 + r)PN + m as there is some inate per capita population change each year (e.g. reproduction), modelled by the term (1 + r)PN, as well as some constant migration at rate m, thanks to conservationalists breeding black-footed ferrets in captivity and then introducing them into the wild population each year after the breeding season). For problems 1, 3, and 4, create a single plot, including a descriptive legend and axis labels. Use the model equation given above to numerically simulate solutions (using for loops) instead of the analytical solution to the model (worked out in another homework problem below). Problem 1: (10 pts) Calculate and plot the number of ferrets over time, if there is no conservation effort (migration) starting from 100 ferrets in year 0, for 15 years total (i.e. up to year 14) with (a) r = 0.0194, (b) r = -0.0324, (c) r = -0.0382. Be sure to show all three solutions on the same plot and don't forget to include a descriptive legend and axis labels. Remember, this is a discrete model, so there should only be values plotted for discrete times N = 0,1,2,... and not in between. Problem 2: (2 pts) Interpret the model parameter r when it is negative in the context of a real-world biological mechanism for this population. What could r