An island is developed for people to live. There are 1 million people move to it as its first immigrants. The theoretical carrying capacity C = 240 million. The growth rate r = - 1.2 The logistic function is R(Pn) =r(1 Pn/C). Suppose each generation is 20 years. a). Use the dynamic system approach to analysis the solution. b). If there are extra 1,500,000 people constantly immigrate to this planet every 20 years, what will happen after a long time? c). What should the largest amount of extra immigrants be allowed every 20 years? d). Following the original model, when population grows, the resources are exhausting, thus the carrying capacity is going down. Suppose, after each generation, the carrying capacity reduces 0.1%, but due to the development of the science and technology, 200,000 extra space for living are created. What is the dynamic system of the carrying capacity and what are its dynamics? e). Following part d), what is the new density-dependent population model? Draw a rough time-series graph for it. f). Try to discuss the dynamics of this new density-dependent population model. An island is developed for people to live. There are 1 million people move to it as its first immigrants. The theoretical carrying capacity C = 240 million. The growth rate r = - 1.2 The logistic function is R(Pn) =r(1 Pn/C). Suppose each generation is 20 years. a). Use the dynamic system approach to analysis the solution. b). If there are extra 1,500,000 people constantly immigrate to this planet every 20 years, what will happen after a long time? c). What should the largest amount of extra immigrants be allowed every 20 years? d). Following the original model, when population grows, the resources are exhausting, thus the carrying capacity is going down. Suppose, after each generation, the carrying capacity reduces 0.1%, but due to the development of the science and technology, 200,000 extra space for living are created. What is the dynamic system of the carrying capacity and what are its dynamics? e). Following part d), what is the new density-dependent population model? Draw a rough time-series graph for it. f). Try to discuss the dynamics of this new density-dependent population model