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Math Help - logistic IVP

  1. #1
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    logistic IVP

    logistic equation \frac {dP}{dt} = rP \left( 1 - \frac PK \right)

    world population in 1990 was about 5.3 billion, with intrinsic growth rate r of 0.0038 per year, assume a carrying capacity K = 100 billion for the world population

    how do i use that to write down the logistic IVP with t=0 in 1990???
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  2. #2
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    Quote Originally Posted by razorfever View Post
    logistic equation \frac {dP}{dt} = rP \left( 1 - \frac PK \right)

    world population in 1990 was about 5.3 billion, with intrinsic growth rate r of 0.0038 per year, assume a carrying capacity K = 100 billion for the world population

    how do i use that to write down the logistic IVP with t=0 in 1990???
    This would be your initial condition P(0) = 5.3
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  3. #3
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    do i then solve the following DE:

    dP/dt = 0.0038P * (1 - (P/100))
    and find the constant using P(0) = 5.3
    and shouldn't P(0) equal 5300000000 or do i just multiply the final answer by 1 billion???
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  4. #4
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    Quote Originally Posted by razorfever View Post
    do i then solve the following DE:

    dP/dt = 0.0038P * (1 - (P/100))
    and find the constant using P(0) = 5.3
    and shouldn't P(0) equal 5300000000 or do i just multiply the final answer by 1 billion???
    Solve what you have. Use P(0)=5.3. The units of P are in billions.
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