An archeologist found that the percentage of carbon-14 in a wooden artifact was 20%of what carbon-14 would have been in the wood when it was cut from the tree

It seems like you're asking about the process of carbon dating, but you haven't provided a specific question. Carbon-14 dating is a method used by archaeologists to determine the age of organic material. When an organism dies, it stops absorbing carbon-14, and the isotope begins to decay at a known rate. By measuring the amount of carbon-14 left in the sample, scientists can estimate when the organism died.

In your case, if an artifact has 20% of the carbon-14 it would have had when the tree it was made from was cut down, we can use the half-life of carbon-14 (about 5730 years) to estimate the age of the artifact.

Here's a step-by-step guide:

1. Understand that every 5730 years, the amount of carbon-14 in a sample is halved. This is the half-life of carbon-14.

2. Calculate how many half-lives have passed if the sample now has 20% of its original carbon-14. This is done by understanding that if one half-life has passed, the sample would have 50% of its original carbon-14. If two half-lives have passed, it would have 25%. So, slightly more than two half-lives have passed for the sample to have 20% of its original carbon-14.

3. Multiply the number of half-lives by the length of a half-life (5730 years) to find the approximate age of the sample.

Without doing the exact math, we can estimate that the artifact is slightly more than 11,460 years old (which is 5730 years x 2).