The answer is 46,000 years.
It can be calculated using the equation:
= decimal amount remaining, where n is a number of half-lives.
Decimal amount remaining is 0.00362 (= 0.362%). Let's calculate number of half-lives.
![(1/2)^{n} =0.00362](https://tex.z-dn.net/?f=%20%281%2F2%29%5E%7Bn%7D%20%3D0.00362)
⇒ ![n*log(1/2)=log(0.00362)](https://tex.z-dn.net/?f=n%2Alog%281%2F2%29%3Dlog%280.00362%29)
⇒ ![n= \frac{log(0.00362)}{log(1/2)}= \frac{log(0.00362)}{log(0.5)}](https://tex.z-dn.net/?f=n%3D%20%5Cfrac%7Blog%280.00362%29%7D%7Blog%281%2F2%29%7D%3D%20%5Cfrac%7Blog%280.00362%29%7D%7Blog%280.5%29%7D%20)
⇒ n ≈ 8
Now we know that number of half-lives is 8.
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 (8). Since 5,730 years × 8 = 45,840 years, then the person died 46,000 years ago (rounded to the nearest thousand).