Final answer:
The age of the fossil is calculated using radiocarbon dating, which involves the half-life of Carbon-14. With only 1/16 of the original C-14 left, the fossil is approximately 22,920 years old, based on the known half-life of 5,730 years for C-14.
Step-by-step explanation:
The process we are dealing with when we talk about the age of a fossil is known as radiocarbon dating, which involves the decay of the radioactive isotope Carbon-14 (C-14). This isotope is useful for dating artifacts that were once living and are not older than about 50,000 years. The relevant concept here is the half-life of C-14, which is the time required for half of the original amount of C-14 to decay, and is known to be approximately 5,730 years.
To calculate the age of a fossil when only 1/16 of the original amount of C-14 remains, we must understand that this represents four half-lives (since 1/2 to the 4th power equals 1/16). Thus, by multiplying the number of half-lives that have passed (4 in this case) by the half-life duration (5,730 years), we get an estimated age for the fossil. Mathematically, this can be shown as:
Number of half-lives (n) = 4
Half-life of C-14 (T) = 5,730 years
Age of the fossil (A) = n × T = 4 × 5,730 years = 22,920 years
Therefore, the fossil is approximately 22,920 years old.