SOLUTION: The Mesopatamian civilization was dated by using the carbon-14 dating. A piece of wood discovered in an archaeological dig was found to have lost 62% of its carbon-14. Determine it

Question 38296: The Mesopatamian civilization was dated by using the carbon-14 dating. A piece of wood discovered in an archaeological dig was found to have lost 62% of its carbon-14. Determine its age.
The answer is 7997 years but I don't know how to get to that answer.
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
you need to know the halflife of C-14. It is 5730 years.

Formula for half-life, T is where y is the "time constant".

We need to figure out the time constant first:

-->
y = 0.000120968 years^(-1)

Right then: exponential decay has a generic formula:

where N is the amount left "now" and is the original amount.

Now, we are told that the carbon14 has reduced by 62%. So, if there was originally 100g of it, there now is 38g... a reduction of 62%. So, we have:

-->

Working this out gives you 7998.7 years, which is in agreement with your answer, assuming rounding errors and the value of the half life used by the question.

jon.

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