Question

The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 66​% of the​ carbon-14 expected in living​ matter, when did the tree​ die?
The tree died about
? years ago
​(Do not round until the final answer. Then round to the nearest whole​ number.)

Answer 1

The tree died about 3357 years ago.

Explanation:

The half life of carbon - 14 is given by

$A(t)=A(0)e^{-kt}$

where $A(t)=0.5$

$A(0)=1$

$t=5600$

Substituting these values in the above equation, we get,

$0.5=1e^{-5600k}$

Taking In on both sides of the equation, we get,

   $In(0.5)=-5600k$

      $\frac{In(0.5)}{-5600} =k$

$0.00012377=k$

Since, only 66% of Carbon - 14 remains after the time T.

Thus, we have,

$0.66=1e^{-kT}$

Taking In on both sides of the equation, we get,

  $In(0.66)=-0.00012377 \ T$

$\frac{In(0.66)}{-0.00012377} = T$

        $3357=T$

Thus, the tree died about 3357 years ago.