An artifact was found and tested for its carbon-14 content. If 81% 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 find the probable age of the artifact, we need to use the concept of half-life in relation to the remaining carbon-14 content.
The half-life of carbon-14 is 5,730 years, which means that after each 5,730 years, half of the original amount of carbon-14 will have decayed.
Given that 81% of the original carbon-14 is still present, we can calculate how many half-lives have passed.
To do this, we'll use the following formula:
Remaining fraction = (1/2)^(number of half-lives)
Solving for the number of half-lives:
0.81 = (1/2)^(number of half-lives)
Taking the logarithm base 2 (since we have a 1/2 fraction):
log2(0.81) = number of half-lives
Using a calculator, we find that log2(0.81) is approximately -0.2802.
Now, we can solve for the number of half-lives:
-0.2802 = number of half-lives
The negative sign indicates that some fraction of a half-life has passed. To find the positive value, we'll multiply by -1:
number of half-lives = 0.2802
To find the age of the artifact, we'll multiply the number of half-lives by the length of one half-life:
age = number of half-lives * half-life
age = 0.2802 * 5,730 years
Using a calculator, we find that the age is approximately 1,619 years.
Therefore, the probable age of the artifact is around 1,619 years (to the nearest 100 years).