Final answer:
Carbon-14 dating is used to determine the age of archaeological finds by comparing the ratio of carbon-14 to carbon-12. In this case, the find is approximately 74,490 years old.
Step-by-step explanation:
Carbon-14 dating is a method used to determine the age of archaeological finds. Carbon-14 has a half-life of 5730 years, meaning that every 5730 years, half of the carbon-14 in a sample decays.
By comparing the ratio of carbon-14 to carbon-12 in a sample to that of a living plant in the same area, we can calculate the age of the find.
In this case, the activity of the live plant is given as 15.6 and the find reads at 0.213 activity.
We can set up a proportion: (0.213/15.6) = (1/2)^n, where n is the number of half-lives that have occurred.
Solving for n, we find that the find is approximately 13 half-lives old.
Therefore, the age of the find is approximately 5730 * 13 = 74,490 years.