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Homework Help: DE Population Models Question

  1. Feb 8, 2010 #1
    Working on some DE homework and need a tad bit of guidance. I got fairly far, I'm just wondering what the next step is.

    1. The problem statement, all variables and given/known data
    The rate of change of an alligator population P is proportional to the square of P. The swamp contained a dozen alligators in 1988, two dozen in 1998. When will there be four dozen alligators in the swamp? What happens thereafter?


    2. Relevant equations
    dP/dt=kP


    3. The attempt at a solution

    Let P=the number of alligators in dozens
    Let t=time in years, where 1988=0

    dP/dt=kP^2

    ∫dP/P^2=∫kdt

    -1/P=kt+C

    P=-1/(kt+C)

    Given that P(0)=1, C=-1

    For P(10)=2, k=1/20 (2=-1/(10k-1))

    So now could I say that P(t)=-1/((t/20)-1), let P(t)=4 and solve for t?

    My concern isn't really to get the answer but that I am not understanding the procedure for this. I feel like I'm just stumbling through.

    Any help is really appreciated greatly. Thanks :)
     
  2. jcsd
  3. Feb 8, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I think you are doing just fine. Yes, set P(t)=4 and solve for t.
     
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