Chapter 5, Problem 93RE

To determine

To find: The approximate years ago the man had died.

Answer to Problem 93RE

The approximate years ago the man had died is $24217.72\text{years}$ .

Explanation of Solution

Given information:

The half life of carbon 14 is $5600\text{years}$ and the bone of the man contain approximately $5\%$ of the original amount of carbon 14.

The rate of decay is calculated as,

  $\begin{array}{l}A=A_0{e}^{rt}\\ \frac{1}{2}{A}_0=A_0{e}^{r\times 5600}\\ \frac{1}{2}=e^{5600r}\\ r=-0.000124\end{array}$

The approximate years ago the man had diedis calculated as,

  $\begin{array}{l}A=A_0{e}^{rt}\\ 0.05A_0=A_0{e}^{-0.0001237t}\\ 0.05=e^{-0.0001237t}\\ t=24217.72\text{years}\end{array}$

Thus, the approximate years ago the man had diedis $24217.72\text{years}$ .