Question

Carbon-14 has a half-life of 5,730 years. If the age of an object older than 50,000 years cannot be determined by radiocarbon dating, then
* carbon-14 levels in a sample are undetectable after approximately ten half-lives.
* carbon-14 levels in a sample are undetectable after approximately nine half-lives.
* the half-life of carbon-14 is too long to accurately date the object.
* a radioisotope with a shorter half-life should be used to date the object.

Answer 1

* carbon-14 levels in a sample are undetectable after approximately nine half-lives.
Nine half-lives pf carbon 14 is 51,570 years.

Source:
https://en.wikipedia.org/wiki/Radiocarbon_dating

Answer 2

C-14 has a half-life of 5730 years. Let's figure out how many half lives would pass in 50,000 years. We take 50,000 and divide it by 5730 = 8.72 half-lives. This is fairly close to 9. The answer is B) C-14 levels in a sample are undetectable after approximately nine half-lives.