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Practical integration

  1. Feb 8, 2008 #1
    1. The problem statement, all variables and given/known data
    a population P(t) is modeled by the equation dP/dt = 0.0004P(P-150), Find a formula which gives the population, P(t), at a general time t.

    2. Relevant equations



    3. The attempt at a solution

    swapping over

    dt=1/0.004P(P-150) dP
    then i integrate both sides

    dt becomes t+c but i'm i'm not sure how to integrate the the dP side, any pointers please?
     
  2. jcsd
  3. Feb 8, 2008 #2

    arildno

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    Are you able to integrate [itex]\int\frac{dx}{x}[/itex]?
     
  4. Feb 8, 2008 #3

    HallsofIvy

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    First, 1/0.004= 250. You have
    [tex]250\int\frac{dP}{P(P-250)}dP[/tex]

    Use "partial fractions". Write
    [tex]\frac{1}{P(P-250)}= \frac{A}{P}+ \frac{B}{P- 250}[/tex]
    Find A and B and do it as two separate integrals.
     
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