A wooden artifact recovered from a tomb contains 29% of the carbon-14 that is present in living trees. The half life of carbon-14 is 5730 years. How long ago was the artifact made?

(1/2)^(t/5730) = .29

(.5)^(t/573) = .29
take logs of both sides and follow rules of logs to get

(t/5730)log.5 = log.29
t/5730 = log.29/log.5
t = appr 10,233 years

To determine how long ago the artifact was made, we need to use the concept of half-life. The half-life of carbon-14 is 5730 years, which means that every 5730 years the amount of carbon-14 in a sample will reduce by half.

In this case, the artifact contains 29% of the carbon-14 found in living trees. This means that 71% (100% - 29%) of the carbon-14 has decayed away over time.

To find out the number of half-lives that have occurred, we can use the following formula:

Number of half-lives = (log(initial amount / final amount)) / (log(1/2))

Since 71% of the carbon-14 has decayed, the final amount is 0.29 (29%). The initial amount is 1 (100%).

Number of half-lives = (log(1 / 0.29)) / (log(1/2))

Using a calculator, we find:

Number of half-lives ≈ 0.712

Since each half-life is 5730 years, we can multiply the number of half-lives by the half-life period to find the age of the artifact:

Age of the artifact ≈ 0.712 * 5730 years

Therefore, the artifact was made approximately 4080 years ago.