To determine how much time has passed when only one-eighth of sodium-24 remains, we can use the concept of half-life.
If the half-life is 15 hours, we can find out how many half-lives have passed to get from the original amount to one-eighth of it.
-
After 1 half-life (15 hours), the amount remaining is: \( \frac{1}{2} \)
-
After 2 half-lives (30 hours), the amount remaining is: \( \frac{1}{4} \)
-
After 3 half-lives (45 hours), the amount remaining is: \( \frac{1}{8} \)
Thus, it takes 3 half-lives to go from the original amount to one-eighth of it.
3 half-lives = 3 × 15 hours = 45 hours.
Therefore, the time that has passed is approximately 45 hours.
The answer is: c) 45 hours.