Final answer:
When one-fourth of carbon-14 remains, two half-lives have elapsed, which would correspond to about 11,460 years if the half-life of carbon-14 is 5,730 years.
Step-by-step explanation:
If one-fourth of the carbon-14 is remaining, it indicates that two half-lives have passed. Since each half-life corresponds to the time it takes for half of the isotope to decay into a more stable form, passing through one half-life would leave us with half (1/2) of the original concentration. After another half-life, we would have half of that amount, leading to a quarter (1/4) of the original concentration remaining. With a known half-life for carbon-14 of 5,730 years, two half-lives would indicate that approximately 11,460 years have passed.