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Perplexing Calculus questions

  1. Feb 17, 2005 #1
    Let P(t) represent the number of wolves in a population at time t years, when t>=0. The population P(t) is increasing at a rate directly proportional to 800 - P(t), where the constant of proportionality is k.

    a) If P(0) = 500, find P(t) in terms of t and k.
    b) If P(2) = 700, find k.
    c) Find lim t -> x P(t)

    I'm really not sure where to start with this question, and any help would be appreciated. It's an entrance exam our teacher got for us to practice on, so I suspect we may not have covered material on these types of questions yet.
  2. jcsd
  3. Feb 17, 2005 #2
    The diff eq:
    dp = k(800-p) dt

    rewrite as:
    dp/(800-p) = k dt

    Then you have to integrate both sides to get something like
    p = 800 - (800-p0)e^-kt
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