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Math Help - transposition of formula

  1. #1
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    transposition of formula

    I've got the following formula

    X=k(1-e^(-t/T)

    i've managed as part of my assignment to find values for all of the constants or variables except t.

    so i now have the formula 10=20(1-e^(-t/0.1)

    could anybody show me how to transpose this formula for t ?
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  2. #2
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    You bet...

    First we need to isolate the term containing the variable.

    10=20(1-e^{-t/.1})

    \frac{1}{2}=1-e^{-t/.1}

    -\frac{1}{2}=-e^{-t/.1}

    \frac{1}{2}=e^{-t/.1}

    taking the natural log of both sides gives.

    ln(1/2)=ln(e^{-t/.1})

    ln(1)-ln(2)= \frac{-t}{.1}ln(e)


    -ln(2)=\frac{-t}{.1}

    solving for t gives...

    .1ln(2)=t
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  3. #3
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    Quote Originally Posted by al2308 View Post
    I've got the following formula

    X=k(1-e^(-t/T)

    i've managed as part of my assignment to find values for all of the constants or variables except t.

    so i now have the formula 10=20(1-e^(-t/0.1)

    could anybody show me how to transpose this formula for t ?
    10 = 20 \left ( 1 - e^{-t/0.1} \right )

    \frac{1}{2} = 1 - e^{-t/0.1}

    e^{-t/0.1} = \frac{1}{2}

    -\frac{t}{0.1} = ln \left ( \frac{1}{2} \right ) = - ln(2)

    t = 0.1 \cdot ln(2)

    -Dan
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