The slope field for the equation dP/dt = 0.0333333P(30 – P), for P≥ 0, is shown below. Pl 11 1 1 1 1 1 1 1 1 38/11/1 717171717 212121}]} 30 On a print out of this slope field, sketch the solutions that pass through (0, 0); (3, 12); (12, 3); (−14.5, 3); (−6, 36); and (−6, 30). For which positive values of P are the solutions increasing? Increasing for: (Give your answer as an interval or list of intervals, e.g., if P is increasing between 1 and 5 and between 7 and infinity, enter (1,5),(7,Inf).) For what positive values of P are the solutions decreasing? Decreasing for: (Again, give your answer as an interval or list of intervals, e.g., if P is decreasing between 1 and 5 and between 7 and infinity, enter (1,5),(7,Inf).) What is the equation of the solution to this differential equation that passes through (0,0)? P = If the solution passes through a value of P > 0, what is the limiting value of P as t gets large? P→

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