An artifact was found and tested for its carbon-14 content. If 71% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years.)

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To determine the probable age of the artifact based on its carbon-14 content, we can use the concept of half-life.

The half-life of carbon-14 is 5,730 years, which means that after this time, half of the original carbon-14 in an artifact will have decayed.

In this case, we are told that 71% of the original carbon-14 is still present. Therefore, we can assume that 29% (100% - 71%) has decayed.

To find the number of half-lives that have occurred, we need to determine how many times 29% can be reduced to 50% (half). This can be calculated as follows:

29% → 50% → 1 half-life
14.5% → 50% → 2 half-lives
7.25% → 50% → 3 half-lives

So, after approximately 3 half-lives, 29% will have decayed to around 7.25%.

Each half-life is equivalent to 5,730 years, so the probable age of the artifact can be calculated by multiplying the half-life by the number of half-lives:

5,730 years x 3 half-lives = 17,190 years

Therefore, the probable age of the artifact, to the nearest 100 years, is 17,200 years.