please read carefully and then answer

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 6: (10 pts) Find an analytical solution to Pn+1 = (1 + r)PN + m (i.e. an expression for Pn that is in terms of only Po, N,r, and m). Use UT EX to present your solution instead of a handwritten derivation. Simplify your expression as much as possible. Hint: You may find the following formula for the partial sum of a geometric series useful 1-x+1 x = 1- x k=0 and the LT EX equation environment align may be helpful, which is demonstrated here: Pn+1 = f(PN) Pn+1 = (1 + r)PN + m In an align environment, creates a new line and & denotes an anchor so that all equations are aligned at that point on each line