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13 Nov 2019
4. (10 marks) Suppose that a population of bacteria grows according to the logistic differential equation = 0.01 Pã¼0.0003P2 dt where P is the population measured in thousands and t is time measured in days. Logistic differential equations are often quite difficult to solve (you can try to solve this one by hand if you have time!). Instead, you will analyze its direction field to acquire information about the solutions to this differential equation a) Calculate the carrying capacity K for this equation? (You must justify your answer by showing how you derived K.) b) What does the carrying capacity represent? c) The direction field for this logistic equation is given below. By studying the direction field determine the values of the population P whern The slopes are close to 0? The solutions are increasing? 30 20 The solutions are decreasing? 6 t (days) d) On the direction field above, sketch and label solutions for initial populations of 0, 10, 20, 40, and 50 equilibrium solutions?
4. (10 marks) Suppose that a population of bacteria grows according to the logistic differential equation = 0.01 Pã¼0.0003P2 dt where P is the population measured in thousands and t is time measured in days. Logistic differential equations are often quite difficult to solve (you can try to solve this one by hand if you have time!). Instead, you will analyze its direction field to acquire information about the solutions to this differential equation a) Calculate the carrying capacity K for this equation? (You must justify your answer by showing how you derived K.) b) What does the carrying capacity represent? c) The direction field for this logistic equation is given below. By studying the direction field determine the values of the population P whern The slopes are close to 0? The solutions are increasing? 30 20 The solutions are decreasing? 6 t (days) d) On the direction field above, sketch and label solutions for initial populations of 0, 10, 20, 40, and 50 equilibrium solutions?
Sixta KovacekLv2
20 Aug 2019