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AP®︎/College Calculus BC

Course: AP®︎/College Calculus BC > Unit 7

Lesson 9: Logistic models with differential equations
Math
AP®︎/College Calculus BC
Differential equations
Logistic models with differential equations
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Differential equations: logistic model word problems

Google Classroom

Problem

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
mice
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