Final answer:
The age of a sample containing 87.5% of the daughter isotope Nitrogen-14 is approximately 17190 years.
Step-by-step explanation:
The age of a sample can be calculated using the equation: how old (time) = n * t₁/2. In this case, the sample contains 87.5% of the daughter isotope Nitrogen-14, which means that 87.5% of the original parent isotope (Carbon-14) has decayed. Since the half-life of Carbon-14 is 5730 years, we can determine the age of the sample by setting up the following equation:
0.875 = 0.5^(t/5730)
By solving for t, we find that the age of the sample is approximately 17190 years, so the correct answer is C. 17190 Years.