5. (14 points) A calculator may be used. The rate of change of the population of moose, M (t), in the Boundary Waters Canoe Area Wilderness is directly proportional to 1200 - M(t), for all t 2 0 . 't' is the time in years and k is a constant of proportionality. When t = 0, the population is 300. a. Write a differential equation that models this situation. b. Determine M(t) in terms of t and k. c. If M(4) = 600 find the value of k. d. Calculate M(8) and explain its meaning in context of the situation. e. Determine lim. M(t) and explain its meaning in context of the situation