Final answer:
The piece of wood that retains 0.7813% of carbon-14 represents about seven half-lives using carbon-14 dating. As one half-life of carbon-14 is 5730 years, the age of the wood would be 7 times 5730, which is approximately 40,110 years.
Step-by-step explanation:
The question involves determining the age of a wooden artifact using the concept of half-life in the context of carbon-14 dating. When a piece of wood retains only 0.7813% of the carbon-14 content found in a living organism, that amount represents approximately seven half-lives of carbon-14, since (1/2)^7 is approximately 0.7813%. Given that each half-life of carbon-14 is about 5730 years, to calculate the number of years, you'd multiply the number of half-lives by the number of years per half-life, which is:
7 (half-lives) × 5730 years (per half-life) = 40,110 years
Therefore, none of the multiple choice options A) 2,570 years, B) 5,140 years, C) 7,710 years, or D) 11,460 years is correct, as the time calculated far exceeds these values. To answer the multiple-choice question accurately, one would require an option that corresponds to approximately 40,110 years, which is the product of the half-lives and the known half-life duration of carbon-14.