Final answer:
The age of the artifact can be calculated by determining the number of half-lives that have passed using the carbon-14 to nitrogen-14 ratio. In this case, the ratio of 13 means that 3 half-lives have passed, making the artifact 17,190 years old.
Step-by-step explanation:
The question involves the concept of radiocarbon dating which is based on the decay of Carbon-14 (14C). The half-life of 14C, as given, is 5730 years. According to the question, the ratio of carbon-14 to nitrogen-14 in an artifact is 13:1.
Since the initial ratio when the organism was alive would have been 1:0 (as nitrogen-14 doesn't form in living tissue), after one half-life, this would become 0.5:0.5 (as half the carbon-14 would have decayed into nitrogen-14), after two half-lives, it would be 0.25:0.75, and after three half-lives, it would be 0.125:0.875, which simplifies to approximately 1:7 (which is the half of 1:14).
This indicates that the artifact underwent three half-lives (3 x 5730 years), aging it to approximately 17,190 years, therefore the correct answer is A. 17,190 years.