Question

An anthropologist finds bone that her instruments measure it as 0.012% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The half life of carbon 14 is 5,730 years. Round your answer to the nearest thousand.(35pts).

Answer 1

The answer is 74,000 years.

It can be calculated using the equation:

 $(1/2) ^{n}$ = decimal amount remaining, where n is a number of half-lives.

Decimal amount remaining is 0.00012 (= 0.012%). Let's calculate number of half-lives.

$(1/2)^{n} =0.00012$

⇒ $n*log(1/2)=log(0.00012)$

⇒ $n= \frac{log(0.00012)}{log(1/2)}= \frac{log(0.00012)}{log(0.5)}$

⇒ n ≈ 13

Now we know that number of half-lives is 13.

Number of half-lives is quotient of total time elapsed and length of half-life.
So, total time elapsed is a product of length of half-life (5,730 years) and number of half-lives (13). Since 5,730 years × 13 = 74,490 years, then the person died 74,000 years ago (rounded to the nearest thousand).