# Question #9dcb1

Jul 13, 2017

The ageof the cloth is $= 7574.6$ years

#### Explanation:

The half life of $C - 14$ is ${t}_{\frac{1}{2}} = 5730 y$

The radioactive constant is $\lambda = \ln \frac{2}{t} _ \left(\frac{1}{2}\right)$

$\lambda = \ln \frac{2}{5730} = 0.000120968 {y}^{-} 1$

${M}_{0} / \left(M \left(t\right)\right) = {e}^{\lambda t}$
$t = \frac{1}{\lambda} \cdot \ln \left({M}_{0} / \left(M \left(t\right)\right)\right)$
$M \left(t\right) = 0.4 {M}_{0}$
$t = 8266.64 \ln \left(\frac{1}{0.4}\right) = 7574.6 y$