Final answer:
The fossil is approximately 3,306 years old.
Step-by-step explanation:
The age of the fossil can be calculated using the known half-life of carbon-14. Carbon-14 has a half-life of 5,730 years, which means that after 5,730 years, only half of the original carbon-14 will remain. Since the fossil contains 70% of its normal amount of carbon-14, we can calculate the age as follows:
- Let's assume the original amount of carbon-14 in the fossil was 100 units.
- After one half-life (5,730 years), half of the carbon-14 will remain, which is 50 units.
- Since the fossil contains 70% of its normal amount, we can calculate the age by dividing the remaining amount (50 units) by 70% (0.7), which gives us approximately 71.43 units.
- Now we can calculate how many half-lives it took for the remaining amount to reach 71.43 units. We divide the remaining amount by the original amount (100 units) and take the logarithm base 0.5 to find the number of half-lives. This gives us approximately 0.576.
- To find the age of the fossil, we multiply the number of half-lives by the length of each half-life (5,730 years), which gives us approximately 3,306 years.
Therefore, the fossil is approximately 3,306 years old.