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Differential Equationshard
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A population P(t)P(t)P(t) satisfies P′=0.5P(1−P/K)P' = 0.5P(1-P/K)P′=0.5P(1−P/K). If the population is at 90%90\%90% of its carrying capacity at t=0t=0t=0, what is the expression for P(t)P(t)P(t)?