Question

A wooden artifact from an ancient tomb contains 55 percent of the carbon-14 that is present in living trees.

How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)

Answer 1

Answer:

$t \approx 4942.105\,years$

Step-by-step explanation:

The half-life of the carbon-14 is 5730 years. The decay model for an isotope is:

$\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }$

The time constant of the carbon-14 is:

$\tau = \frac{5730\,years}{\ln 2}$

$\tau = 8266.643\,years$

The time of the artifact is:

$\ln \frac{m}{m_{o}} = -\frac{t}{\tau}$

$t = -\tau \cdot \ln \frac{m}{m_{o}}$

$t = - (8266.643\,years)\cdot \ln 0.55$

$t \approx 4942.105\,years$