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Math Help - Reducing non-linear laws to linear fractions

  1. #1
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    Reducing non-linear laws to linear fractions

    current in mA flowing through a capacitor is discharging over time ms, as shown
    i 203 61.14 22.49 6.13 2.49 0.615
    t 100 160 210 275 320 390

    the graph follows the law of, i = Ie^-t/T (e refers to log, and its to the power of -t/T)

    find values for I and T

    my solution

    log i = log I e ^ -t/T

    log i = log I + log e ^ -t/T

    log i = -t / T log I
    Y = M X + C

    i then plot the graph of log of Y against x (shown in attachment)

    so - t should = change in log Y / change in x

    -t = 3.2 / 392 = 8.16*10^-3

    log I = point of intersect 3.2

    I = e3.2

    I = 24.53
    t = 8.16*10^-3
    i do this and then put the values into the forumla

    24.53e^((8.16*10^-3)/t) = i

    but am not getting the correct answers if t is 100 it should be 203 but i get 24.53


    any help on where iv gone wrong would be helpful
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  2. #2
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    Re: Reducing non-linear laws to linear fractions

    I graphed i vs. \log(t) in my TI-83

    linear regression yielded the equation \log(i) = -0.200 t + 7.313

    I = i(0) = e^{7.313} \approx 1500

    i(t) = I \cdot e^{-.02t}

    i(100) = 203
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