1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: DE Population Models Question
  1. Modeling with DE's (Replies: 4)

  2. Population Model (Replies: 2)

  3. Population model (Replies: 1)

Loading...