Hello, I need help on these calculus problems.

Calculai Mariman WS 5.5: Partial Fractions & Logistic 5. The population P(r) of a species satisfies the logistic differential equation 12-P where 5000 the initial population is P(0) = 3000 and t is the time in years. What is lim P()? (A) 2500 (B) 3000 (C) 4200 (D) 5000 (E) 10,000 H 6. Suppose a population of wolves grows according to the logistic differential equation de = 3P-0.01p. dr where P is the number of wolves at time t, in years. Which of the following statements are true? I. lim P() = 300 II. The growth rate of the wolf population is greatest when P = 150. III. If P > 300, the population of wolves is increasing. (A) I only (B) II only (C) I and II only (D) II and III only (E) I, II, and III9. Suppose the population of bears in a national park grows according to the logistic differential equation dp - = 5P -0.002p , where P is the number of bears at time t in years. (a) If P(0) = 100, then lim P(() =_ Sketch the graph of P() . For what values of P is the graph of P increasing? decreasing? Justify your answer. (b) If P(0) = 1500, lim P(1) = Sketch the graph of P(). For what values of P is the graph of P increasing? decreasing? Justify your answer. (c) If P(0) = 3000, lim P(1) = Sketch the graph of P(r) . For what values of P is the graph of P increasing? decreasing? Justify your answer. (d) How many bears are in the park when the population of bears is growing the fastest? Justify your