Final answer:
The age of the sample can be determined using radiometric dating and the concept of half-life. The correct answer is option 1: 5730 years.
Step-by-step explanation:
The age of a sample that contains 87.5% of the daughter isotope Nitrogen-14 can be determined by using radiometric dating and the concept of half-life.
The half-life of Carbon-14 (¹⁴C) is approximately 5,730 years.
This means that after 5,730 years, half of the original ¹⁴C will have decayed to ¹⁴N. Since Nitrogen-14 is the daughter isotope, it is safe to assume that the original isotope is Carbon-14.
Therefore, the correct answer is Option 1: 5730 Years.