To determine the age of the bone, we need to use the concept of carbon dating. Carbon dating relies on the fact that carbon-14 (C-14) is a radioactive isotope that decays over time.
The half-life of carbon-14 is approximately 5730 years, which means that after this time, half of the carbon-14 in a sample will have decayed.
If we assume that the bone initially had its normal amount of carbon-14, then after one half-life (5730 years), the bone would have 50% of its original carbon-14 remaining.
Since the bone was found to have only 20% of its normal amount of carbon-14, we can use this information to calculate the approximate age.
Let's denote the number of half-lives as 'n'.
Given that the bone has 20% of its original carbon-14, it means that it has gone through four half-lives (50% * 50% * 50% * 50% = 0.20 or 20%).
To find the age, we multiply the number of half-lives (n) by the half-life of carbon-14 (5730 years):
n * 5730 years = 4 * 5730 years = 22,920 years
Therefore, based on the 20% remaining carbon-14, the bone is approximately 22,920 years old.