To determine how many half-lives have occurred after 67.5 hours, you can divide the total time elapsed by the half-life of the radioisotope.
Given:
- Half-life = 7.5 hours
- Total time = 67.5 hours
Number of half-lives = Total time / Half-life
\[ \text{Number of half-lives} = \frac{67.5 \text{ hours}}{7.5 \text{ hours}} = 9 \]
Therefore, the answer is:
c. 9 half-lives