5. There are 100 deer in a forest. The population of deer follows the logistic growth model: P P(0) = 100 K where P(t) is the population of deer at time t and K is a constant (capacity). (a) The forest is the perfect place for deer. Solve the equation assuming K and find P(t). What is the population of deer in the long run? In other words, find lim P(t). = 200 dP dt 0047 = = P(1 (hint: You can assume |P(t)| = P(t) 0 and |200 P(t)| = 200 P(t) 0.) (b) Due to global warming, the forest has turned into a desert. Solve the equation assuming K 50 and find P(t). What is the population of deer in the long run? In other words, find lim P(t). = t (hint: You can assume |P(t)| = P(t) 0 and [50 P(t)| = P(t) 50 0.)