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Math Help - integration

  1. #1
    Junior Member
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    integration

    Forgive me If I'm posting in the wrong thread, but I did derive this problem after separation of variables and partial fractions..
    I'm more or less questioning whether I manipulated the following equation correctly:

    Say I have (1/(Ps - Pu))ln[(P - Pu)/(Ps - P)] = (r/k)t + C.
    I'm trying to find t.

    Provided the values; The constant eort model also has r = 0:3 per year, K = 3000 kilotons and PS = 1600 kilotons but PU = 0 kilotons. Assuming the same initial condition of P = 1410 when t = 0 calculate the time taken for the population to reach P = 1500 for this model.


    [1/(1600 - 0)]ln[(1410 - 0)/(1600 - 1410)] = (0.3/3000)0 + C

    (1/1600)*ln(1410/190) = C ---> C = ln(1410/190) /200

    So to find t so that P(t) = 1500 we have


    (1/1600)ln(1500/100) = (0.3/3000)t + [(1/1600)*ln(1410/190)

    0.00169253137 = (0.3/3000)*t + 0.00125270057
    -0.00125270057 -0.00125270057
    0.0004398308 = (0.3/3000)t

    t = (3000/0.3) * 0.0004398308 = 4.40 years.
    Last edited by cellae; October 1st 2012 at 10:03 PM.
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  2. #2
    MHF Contributor
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    Re: integration

    Hey cellae.

    Didn't you post this in Physics Forums?
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  3. #3
    Senior Member MaxJasper's Avatar
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    Re: integration

    t=4.3983080 or 4.4 is OK.
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