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Math Help - Exponential Decay

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    Exponential Decay

    How old is a piece of wood that has lost 90% of its carbon-14?

    I know that there is only a presence of 10% but don't know how to find the decay rate (k).
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  2. #2
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    Quote Originally Posted by littlesohi View Post
    How old is a piece of wood that has lost 90% of its carbon-14?

    I know that there is only a presence of 10% but don't know how to find the decay rate (k).
    1. The half-life time of carbon-14 is 5730 years.

    2. Use the equation:

    A(t)=A_0 \cdot e^{k \cdot t} to calculate k,

    where A(t) is the present amount and A_0 the initial amount.

    3.  \frac12 A_0 = A_0 \cdot e^{k \cdot 5730}~\implies~k= \dfrac{\ln\left(\frac12\right)}{5730}

    4. Solve the following equation for t:

    \frac1{10} A_0=A_0 \cdot e^{\frac{\ln\left(\frac12\right)}{5730} \cdot t}

    Spoiler:
    I've got 19,035 years
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