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Math Help - Not sure If I manipulated this equation properly..

  1. #1
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    Not sure If I manipulated this equation properly..

    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) /1600

    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 11:38 PM.
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  2. #2
    Senior Member MaxJasper's Avatar
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    Re: Not sure If I manipulated this equation properly..

    t=4.4 is OK
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