00:03
So we have a carbon -14 dating problem, and we're going to use our radioactive decay model, exponential model, m -equals m -0 -e to the k -t.
00:13
Initially, we're going to use the half -life information to find the value of k, and then once we know that, we'll be able to answer the question.
00:21
So for the half -life, we're going to use m -0 as the initial amount, and then we can use half of m -k -not as the final amount.
00:28
Put that into the equation, and we put the half -life in for the time, and we can solve for k -n -n -south.
00:33
So those are the numbers plugged into our model.
00:36
So let's divide both sides of the equation by m not, and we get one half, which i'll just write as 0 .5, equals e to the 5 ,730k.
00:46
Now we take the natural log of both sides, and we divide both sides by 5 ,730, and our value of k is natural log of 0 .5 over 5 ,730.
00:58
So that goes into the model, and now our model is m equals n -not, m -not, e to the the natural log of 0 .5 over 5 ,730 times t.
01:10
So we're going to use that model as we move forward.
01:14
So now we know that the sample of parchment had 74 % of the normal amount of carbon 14 in a living plant...