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Differential equations: logistic model word problems


The population P(t) of mice in a meadow after t years satisfies the logistic differential equation dPdt=3P(1P2500) where the initial population is 1000 mice.
What is the population when it's growing the fastest?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi