An artifact was found and tested for its carbon-14 content. If 88% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? Use that carbon-14 has a half-life of 5,730 years.
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To determine the probable age of the artifact, we need to use the concept of carbon-14 dating and its half-life.
The half-life of carbon-14 is 5,730 years, which means that after this period, only half of the carbon-14 in a sample remains.
In this case, the artifact was tested and found to still have 88% of its original carbon-14 content. To find its probable age, we can calculate how many half-lives have passed.
Let's assume that the original amount of carbon-14 in the artifact was 100%.
After one half-life (5,730 years), 50% of the original carbon-14 would remain.
After two half-lives (2 x 5,730 years = 11,460 years), 25% of the original carbon-14 would remain.
After three half-lives (3 x 5,730 years = 17,190 years), 12.5% of the original carbon-14 would remain.
And so on.
Since we know that 88% of the original carbon-14 is still present, we can set up the equation:
(0.88) * (100%) = (0.50) ^ n
Where n represents the number of half-lives that have passed.
To solve for n, we can take the logarithm of both sides:
log ((0.88) * (100%)) = log ((0.50) ^ n)
Using logarithmic properties, we can bring down the exponent:
log (0.88) + log (100%) = n * log (0.50)
We can calculate the left side of the equation:
log (0.88) ≈ -0.056
And the right side of the equation:
log (0.50) ≈ -0.301
Now we can solve for n:
-0.056 + log (100%) = n * (-0.301)
-0.056 = n * (-0.301)
n ≈ -0.056 / (-0.301)
n ≈ 0.186
Since n represents the number of half-lives, we can round up to the nearest whole number. Therefore, the probable age of the artifact is approximately 1 half-life or 5,730 years.
Please note that this is an approximate calculation and assumes that the decay rate has remained constant throughout history.