A specimen has .625 the amount of carbon 14 you would find in a living specimen.
How many half-lives has the specimen been through?
How old is the specimen?
3900 years. The half life of C-14 is 5730 years.
3900/5730 is the number of half-lives in the age
To determine the number of half-lives the specimen has been through, we can use the following formula:
Number of Half-Lives = log (Amount of Carbon 14 Remaining / Initial Amount of Carbon 14) / log (0.5)
Given that the amount of carbon 14 in the specimen is 0.625 times the amount found in a living specimen, we can calculate the number of half-lives:
Number of Half-Lives = log (0.625) / log (0.5)
Using a logarithmic calculator or software, we find that log (0.625) ≈ -0.2041 and log (0.5) ≈ -0.3010.
Number of Half-Lives = -0.2041 / -0.3010 ≈ 0.678
Therefore, the specimen has been through approximately 0.678 half-lives.
To calculate the age of the specimen, we need to know the half-life of carbon 14. The half-life of carbon 14 is approximately 5730 years.
Age of the Specimen = Number of Half-Lives * Half-Life of Carbon 14
Age of the Specimen = 0.678 * 5730 years
Using a calculator, we get:
Age of the Specimen ≈ 3885.54 years
Therefore, the specimen is approximately 3885.54 years old.