To determine how many half-lives have occurred after 67.5 hours for a radioisotope with a half-life of 7.5 hours, you can use the following formula:
Number of half-lives = Total time elapsed / Half-life duration
Plugging in the values:
Number of half-lives = 67.5 hours / 7.5 hours = 9
So, the answer is:
c) 9 half-lives