Question 2 (12 marks) Suppose that the number of mice per hectare P(t) at time t is modelled by the logistic equation dP = 0.0005P(2000 - P) where t is time in months. a. If initially there are 100 mice per hectare, solve the differential equation to find P(t) . (4 marks) b. Draw a neat, accurate sketch of P(t) over the first 12 months by hand, or using Maple or other software. However you do it, you must include accurate grid markers, label the axes, and include important features such as asymptotes. (3 marks) c. Mice are considered a plague when the population density reaches 1000 per hectare. Calculate how many months it will take until this density is reached. (3 marks) d. State the value the population density tends to over the long term, that is, lim P(t) . (2 marks)