Final answer:
The age of the charcoal can be determined using the concept of radioactive decay and half-life. By calculating the number of half-lives the charcoal has undergone, we can estimate its age. In this case, the charcoal is approximately 22,860 years old.
Step-by-step explanation:
To determine the age of the charcoal, we can use the concept of radioactive decay and half-life. Carbon-14 has a half-life of 5715 years, which means that after 5715 years, half of the original amount of carbon-14 will have decayed. If the charcoal has 20% of its original amount of carbon remaining, we can calculate the number of half-lives it has undergone.
Let's assume the original amount of carbon-14 in the charcoal was 100 grams. After one half-life, it would have decayed to 50 grams. After two half-lives, it would have decayed to 25 grams, and so on.
Since the charcoal has 20% of its original amount remaining, it means it has undergone four half-lives. Therefore, the age of the charcoal can be calculated as 4 x 5715 years = 22,860 years.