Final answer:
To determine the age of the fossil, we need to calculate the number of half-lives that have passed. If one half-life is about 500 years and the fossil has 6.25% of its original radioactive isotopes remaining, we can calculate that the fossil is approximately 937.5 years old.
Step-by-step explanation:
To determine the age of the fossil, we can use the concept of half-life. The half-life is the time it takes for half of the radioactive isotopes to decay. In this case, if one half-life is about 500 years and the fossil has 6.25% of its original radioactive isotopes remaining, we can calculate the number of half-lives that have passed.
First, let's find the number of half-lives. If 6.25% of the radioactive isotopes are remaining, it means that 93.75% (100% - 6.25%) have decayed. We can express this as a decimal by dividing 93.75% by 100: 0.9375.
Next, we can determine the number of half-lives by dividing 0.9375 by 0.5 (since half of the radioactive isotopes decay in each half-life): 0.9375/0.5 = 1.875. This means that approximately 1.875 half-lives have passed since the formation of the fossil.
Finally, we can calculate the age of the fossil by multiplying the number of half-lives by the length of one half-life: 1.875 x 500 years = 937.5 years. Therefore, the fossil is approximately 937.5 years old.