If you think you can do it.

I need it to be done within 2 days

Let P=P(t) denote the population of a rare bird species on the island, where t is the time, in years. Suppose M equals the maximum number of sustainable birds and m equals the minimum population, below which the species becomes extinct. The population P can be modeled by the differential equation. dPkM PP E ( )( m) Where k is a positive constant. 1.Suppose the maximum population M is 1200 birds and the minimum population m is 100 birds. If k=0.001, write the differential equation that models the population P=P(t). 2.So|ve the differential equation. 3.lf the population at time t=0 is 300 birds, find the particular solution of the differential equaon. 4.How many birds will exist in 5 years? 5.Using graphing technology, graph the solution found in problem 3. 6.The graph from problem 3 seems to have an inflection point. Approximate the inflection point from the graph. 7.What conclusions can you draw about the rate of change ofthe bird population