Final answer:
To calculate the age of the fossil with 1/8 the original 14C, we determine that it has undergone three half-lives, each of 5,730 years, making the fossil approximately 17,190 years old.
Step-by-step explanation:
The question involves determining the age of a fossil using the concept of half-life in the context of Carbon-14 (14C) dating. To find the age of the fossil when it contains 1/8 of the original amount of 14C, we use the half-life of 14C, which is approximately 5,730 years. Since 1/8 is 2^-3, this represents three half-lives (since (1/2)^3 = 1/8). Therefore, we multiply the number of half-lives by the half-life duration: 3 × 5,730 years = 17,190 years. Hence, the fossil is approximately 17,190 years old.