The population P of some rare rabbits in a small island is given by: where M is the carrying capacity. M represents the maximum sustainable number of rabbits in the island, and k is a constant which may be positive or negative, based on whether the number of rabbits grows or decays. (a) The island has an initial population of 100 rabbits, and after one year, the population increases to 300 rabbits. Solve this differential equation in the case in which the island has a carrying capacity of 1900. Give the answer in terms of time t only. (b) What is the rabbit population after 5 years