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Math Help - Applications of Nonlinear Equations

  1. #1
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    Applications of Nonlinear Equations

    Hello,
    I am having trouble with this problem, but I am sure that I am just making a dumb mistake...

    Find C(t) from dC/dt = C(1-.0005C), C(0) = 1

    First you use partial fractions to get: ((1/C) + (.0005/(1-.0005C))dC = dt

    After that, I integrated the fractions to get:

    ln (C) + .0005(ln(1-.0005)) = t + d d is a constant

    But my books says the second natural log: .0005(ln(1-.0005)), should be negative, and then from there on I am completely stuck... Could anyone tell me how to do this?
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  2. #2
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    Quote Originally Posted by collegestudent321 View Post
    Hello,
    I am having trouble with this problem, but I am sure that I am just making a dumb mistake...

    Find C(t) from dC/dt = C(1-.0005C), C(0) = 1

    First you use partial fractions to get: ((1/C) + (.0005/(1-.0005C))dC = dt

    After that, I integrated the fractions to get:

    ln (C) + .0005(ln(1-.0005)) = t + d d is a constant

    But my books says the second natural log: .0005(ln(1-.0005)), should be negative, and then from there on I am completely stuck... Could anyone tell me how to do this?
    We have:

    d(1-0,0005c) =-0,0005dc and deviding by (1-0.0005c) we have:


    -\frac{d(1-0,0005c)}{(1-0,0005c)} =\frac{0,0005dc}{(1-0,0005c)}. Now substitute in the original equation and integrate
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  3. #3
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    What do the commas mean? I don't think i understand that
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  4. #4
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    oh wait, nevermind, now i know, hahah sorry
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