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Suppose that a population develops according to the logistic equation 3 = 0.02.0 0.000202 dt where t is measured in weeks. (a) What is the carrying capacity? M=v What is the value of k? k=_ (b) A direction field for this equation is shown. 150- 125) 100 75- 25 50 100 150 Where are the slopes close to 0? (Enter your answers as a comma-separated list.) P = Where are they largest? (Enter your answers as a comma-separated list.) P = Which solutions are increasing? (Enter your answer using interval notation.) POE Which solutions are decreasing? (Enter your answer using interval notation.) POE(c) Use the direction eld to sketch solutions for initial populations of 20, 40, 60, 80, 120, and 140. What do these solutions have in common? How do they differ? O All of the solutions have an inflection point. The solutions differ since for 0 100 they are decreasing. Also some of the solutions approach P = 100 as 1' increases and some don't. O None of the solutions have an inflection point. The solutions differ since for 0 100 they are decreasing. Also some of the solutions approach P = 100 as t Increases and some don't. 0 All of the solutions approach P = 100 as t increases. The solutions differ since for 0 100 they are decreasing. Also, some have an Inflectlon point and some don't. 0 All of the solutions approach P = 100 as t increases. Also all the solutions are decreasing. The solutions differ since some have an Inflectlon point and some don't. 0 All of the solutions approach P = 100 as t increases. Also all the solutions are increasing. The solutions differ since some have an inflection point and some don't. Which solutions have inflection points? At what population levels do they occur? 0 The solutions which have P0 = 20 and P0 = 40 have Inflectlon points at P = 50. O The solutions which have P0 = 20, P0 = 40, P,J = 60, and P0 = 80 have inflection points at P = 50. 0 All of the solutions have Inflectlon points at P = 100. O The solutions which have P0 = 120 and P0 = 140 have inflection points at P = 100. 0 None of the solutions have Inflectlon points. --Select--- no solutions (d) What are the equilibrium solutions? (Enter your answers as a c P _ only the increasing solutions all nonzero solutions How are the other solutions related to these solutions? only the decreasing solutions solutions move away from P = 0, and approach P = 100 as t > oo