The ratio of carbon-14 to carbon-12 in a piece of charcoal from a fire pit in an archaeological excavation is found to be 12.5% of that in a sample of modern wood. Approximately how old is the site? (Carbon-14 half-life is 5730 years.) Answer as a whole number with no units.

17190 years          

Explanation:

The exponential decay equation is:

Where:

N(t) is the quantity at time t

N₀ is the initial amount

λ is the decay constant = ln(2)/t(1/2)

t(1/2) is the half-life    

Since the ratio of carbon-14 to carbon-12 is 12.5%, we have that:

By solving the above equation for t:

Therefore, the site is 17190 years old.  

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