To estimate the age of the archaeological sample based on its remaining radioactivity, we can use the concept of half-lives.
The half-life of C-14 is 5470 years. If the sample has one-quarter of its original radioactivity remaining, it means that two half-lives have passed (since after one half-life, 1/2 remains, and after the second half-life, 1/4 remains).
Thus:
- After 1 half-life (5470 years), 1/2 of the original C-14 remains.
- After 2 half-lives (2 * 5470 years), 1/4 of the original C-14 remains.
Calculating the time for two half-lives:
\[ 2 \times 5470 \text{ years} = 10940 \text{ years} \]
Therefore, the best estimate for the age of the archaeological sample is:
B. 10940 years.