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:
$\displaystyle A(t)=A_0 \cdot e^{k \cdot t}$ to calculate k,
where A(t) is the present amount and $\displaystyle A_0$ the initial amount.
3. $\displaystyle \frac12 A_0 = A_0 \cdot e^{k \cdot 5730}~\implies~k= \dfrac{\ln\left(\frac12\right)}{5730}$
4. Solve the following equation for t:
$\displaystyle \frac1{10} A_0=A_0 \cdot e^{\frac{\ln\left(\frac12\right)}{5730} \cdot t}$
Spoiler: