An anthropologist finds there is so little remaining Carbon-14 in a prehistoric bone that instruments cannot measure it. This means that there is less than 0.5% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die? Round your answer to the nearest thousand. (22,000, etc)
To determine how long ago the person died, we can use the concept of half-life in radiocarbon dating. Carbon-14 has a half-life of approximately 5,730 years. This means that after every 5,730 years, half of the Carbon-14 in a sample will decay.
In this case, we are given that there is less than 0.5% of the original Carbon-14 remaining. This corresponds to less than half of the remaining Carbon-14, which indicates that more than one half-life has passed since the person died.
To calculate the number of half-lives that have passed, we can use the following formula:
Number of half-lives = log(remaining amount / original amount) / log(1/2)
Since the remaining amount is less than 0.5% or 0.005 of the original amount, the formula becomes:
Number of half-lives = log(0.005) / log(1/2)
Using a scientific calculator, we find that the number of half-lives is approximately 6.58.
To find the elapsed time, we multiply the number of half-lives by the half-life of Carbon-14:
Elapsed time = 6.58 * 5,730 years
This gives us an elapsed time of approximately 37,647 years.
Finally, rounding to the nearest thousand, we get an answer of approximately 38,000 years ago.