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Differential equations: logistic model word problems


The population P, left parenthesis, t, right parenthesis of mice in a meadow after t years satisfies the logistic differential equation start fraction, d, P, divided by, d, t, end fraction, equals, 3, P, dot, left parenthesis, 1, minus, start fraction, P, divided by, 2500, end fraction, right parenthesis 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, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text