ii. What is the carrying capacity N of Loompaland? iii. In what year will the population reach 99% of N? dp rp(1 ). dt N (Help: The relative growth rate r for the logistic model (2) is r = 0.031476.) The infamous chocolatier Willy Wonka reopens his chocolate factory and starts hiring Ooompa Loompas, who emigrate from Loompaland at a rate proportional to the population p. i. Modify the logistic ODE (2) to include emigration at a rate proportional to the population p. ii. Non-dimensionalise your model in (c)i. by introducing non-dimensional pa- rameters: x = T = rt. iii. Using the linear stability criteria and phase lines, analyse your non-dimensional emigration model for all possible scenarios. iv. What do your results tell you about the future population of Loompaland?