How long ago was the tree burned to make charcoal?

Question

Carbon 14 dating assumes that the carbon dioxide on earth today has the same radioactive content as is did centuries ago. If this is true, the amount of carbon 14 absorbed by a tree that grew several centuries ago should be the same as the amount of carbon 14 absorbed by a tree growing today. A piece of ancient charcoal contains only 15% as much radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make charcoal? Assume the half-life of carbon 14 to be 5730 years.

Answer 1

half life = 5730 years which means 50% of tree will decay in 5730 years. So, in 2*5370 years 50%*50% = 25% will be left and so on. So the formula would be:

(50%)^N = % left = 0.15
to solve do:
log(50%^N) = log(0.15)
N*log(50%) = log(15%)
N = log(15%) / log(50%) = 2.737

so you will have 15% left in 2.737 half lives or
2.737*5730 years = 15,683 years

Answer 2

Multiply the number of "half lives" that make up 15percent by the years in a "half life".

NHL :: (1/2)^NHL = .15

NHL * ln(1/2) = ln(.15)

NHL = ln(.15) / ln(.5) = -1.9 / -.7 = 2.736

years = 5730 * 2.736 = 15683 years

check:

reduced to 50% in 1st half life
reduced to 25% in second half life
resuced to 12.5% in third half life

somewhere between 2-3 half lives, tending tward 3. Checks!

Answer 3

If you believe in the Bible, there must be something wrong with carbon dating. Although, I don't know what part is incorrect.