Question: 11. (5 points each, 20 points in all) Consider the logistic differential equation dy dt = $ (6 - y). Let y = f(t) be

11. (5 points each, 20 points in all) Consider the logistic

11. (5 points each, 20 points in all) Consider the logistic differential equation dy dt = $ (6 - y). Let y = f(t) be the particular solution to the differential equation with f (0) = 8. (a) What is the range of f for t 2 0? (b) Use Euler's method, starting at t = 0 with two steps of equal size, to approximate f (1). (c) A slope field for this differential equation is given below. Sketch possible solution curves through the points (3, 2) and (0, 8). If . (d) Assuming that f(0) = 4 instead, solve the differential equation explicitly for f (t)

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