The graph shows the radioactive decay of a bone that is found to contain 1/8 of the carbon-14 found in living animals today.

Question

Approximately how old is the bone?

a
22,920 years
b
5,730 years
c
11,460 years
d
17,190 years

Answer 1

To determine the age of the bone based on the decay of carbon-14, we can use the fact that the half-life of carbon-14 is approximately 5,730 years.

1. Starting amount: Let's say a living organism has 100% of carbon-14.
2. After 1 half-life (5,730 years): 50% remains.
3. After 2 half-lives (11,460 years): 25% remains.
4. After 3 half-lives (17,190 years): 12.5% remains.
5. After 4 half-lives (22,920 years): 6.25% remains.

If the bone contains 1/8 (12.5%) of the original carbon-14, this corresponds to 3 half-lives.

Calculating the total time from the number of half-lives:

• 3 half-lives × 5,730 years/half-life = 17,190 years.

Therefore, the approximate age of the bone is 17,190 years, so the correct answer is d. 17,190 years.