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Math Help - differencial equation

  1. #1
    Junior Member cinder's Avatar
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    differencial equation



    Can someone give me a starting point?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by cinder View Post


    Can someone give me a starting point?
    Here's the first part:

    \frac{dV}{dt} = -0.03V

    \frac{dV}{V} = -0.03dt

    \int_{V_0}^V \frac{dV}{V} = -0.03 \int_0^t~dt

    ln(V)|_{V_0}^V = -0.03t|_0^t

    ln(V) - ln(V_0) = -0.03t

    ln \left ( \frac{V}{V_0} \right ) = -0.03t

    V = V_0e^{-0.03t}

    -Dan
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by cinder View Post


    Can someone give me a starting point?
    Here's the second part.

    Dan provided the equation for V(t)

    It is V(t) = V_0 e^{-0.03t}

    Now we want t such that V(t) is 25% of it's original value, in other words, we want t when

    V(t) = 0.25V_0

    So our equation becomes

    0.25V_0 = V_0 e^{-0.03t}

    \Rightarrow 0.25 = e^{-0.03t}

    \Rightarrow t = - \frac {\ln 0.25}{0.03}
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  4. #4
    Junior Member cinder's Avatar
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    Thanks for the help, I think I got it!
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