Final answer:
To estimate the age of charcoal from radiocarbon dating, one uses the half-life of carbon-14, which is 5,730 years. If charcoal contains 1/1000th the C-14 of a living tree, it is approximately 57,300 years old, as ten half-lives would have passed.
Step-by-step explanation:
To determine the approximate age of a tree from which a piece of charcoal was made, based on its carbon-14 content, we use the principles of radiocarbon dating. The half-life of carbon-14 (C-14) is 5,730 years, which implies that every 5,730 years, the quantity of C-14 in a sample is reduced by half.
As an example, let's say a sample of charcoal is found to contain 1/1000th the C-14 a living tree would. To calculate the age of the charcoal, we note that 210 equals 1024, which is approximately 1/1000. Since each half-life is 5,730 years, and it takes 10 half-lives to reach a 1/1000th amount of C-14, we can estimate that the sample is around 57,300 years old (10 half-lives × 5,730 years/half-life).