A wooden artifact from an ancient tomb contains 50 percent of the carbon-14 that is present in living trees. How long ago, to the nearest year, was the artifact made? (The half-life of carbon-14 is 5730 years.)
To determine the approximate age of the artifact, we need to use the concept of carbon-14 dating and the half-life of carbon-14.
The half-life of carbon-14 is the time it takes for half of the carbon-14 in a sample to decay. In this case, the half-life of carbon-14 is given as 5730 years.
Since the artifact contains 50 percent of the carbon-14 found in living trees, it indicates that half of the original carbon-14 has decayed over time.
To find the age of the artifact, we can set up the following equation:
(Initial amount of carbon-14) * (0.5)^n = (Current amount of carbon-14)
Where "n" represents the number of half-lives that have passed.
Since the artifact contains exactly half of the original carbon-14, we can substitute the values into the equation:
(0.5)^(n) = 0.5
To solve for 'n', we can take the logarithm of both sides of the equation:
log((0.5)^(n)) = log(0.5)
n * log(0.5) = log(0.5)
Using logarithmic properties, we can rewrite the equation as:
n = log(0.5) / log(0.5)
By dividing the logarithm of 0.5 by the logarithm of 0.5, we get:
n = 1
Since 'n' represents the number of half-lives, and we determined that 1 half-life has passed, we can conclude that the artifact is approximately one half-life old.
Since each half-life of carbon-14 is 5730 years, to find the age of the artifact, we multiply the half-life by 'n':
5730 years * 1 = 5730 years
Therefore, the artifact was made approximately 5730 years ago, to the nearest year.