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Dfq Prob, using Logisitc Equation

  1. Apr 3, 2005 #1
    Q. Develop the model of the logisitic equation and use it to solve the following. At first there are 100 fruit flies. After one day there are 200 fruit flies.The maximum population is 10,000 fruit flies.

    a) Determine the population size P as a function of days t.

    We know,

    P(0) = 100

    P(1) = 200

    P max = 10,000

    Logisitc equation:

    dP/dt = kP ( 1-P/Pmax)

    Integrating both sides:

    Integral ( dP/P(1-P/m) = Integral kdt

    Using Partial fractions, we get:

    PMax - P^2 = Ce^kt

    Therefore,

    C = PM - P^2 / e^kt

    P(t) = Ce^kt / Pmax - P

    Is this correct,

    b. How many flies are present after 3 days?

    For, this we can find C, using the initial condition: P(0) = 100

    To find k, we can use P(1) = 200, and Pmax = 10,000

    After finding all this,

    We can do, P(3) = Ce^kt / Pmax - P

    Any suggestions / ideas, Please help
     
  2. jcsd
  3. Apr 3, 2005 #2
    Please note, that M , in the previous parts, is actually referring to Pmax
     
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