Work the following on notebook paper. Use your calculator on 4(b) and 4(c) only. 1. Suppose the population of bears in a national park grows according to the logistic differential equation (jgP = SID0.002132 , where P is the number of bears at time t in years. I (a) If P(0) :100, nd lirn P(t). Is the solution curve increasing or decreasing? I}:rc Justify your answer. Sketch the graph of PU). (b) If 10(0) = 1500, nd lirn P(t). Is the solution curve increasing or decreasing? rm Justify your answer. Sketch the graph of P(t). (c) If P(0) = 3000, find lim P(r). Is the solution curve increasing or decreasing? IMo Justify your answer. Sketch the graph of P(I). (d) How many bears are in the park when the population of bears is growing the fastest? Justify your