Final answer:
To determine the percentage of a sample of iodine-125 that would be left after 30.8 days, we need to calculate the number of half-lives that occur within that time period. The half-life of iodine-125 is 60.25 days. The percentage of the sample remaining can be calculated by raising 0.5 to the power of the number of half-lives and multiplying by 100.
Step-by-step explanation:
To determine the percentage of a sample of iodine-125 that would be left after 30.8 days, we need to calculate the number of half-lives that occur within that time period. The half-life of iodine-125 is given as 60.25 days. To calculate the number of half-lives, we divide the time period by the half-life:
Number of half-lives = 30.8 days / 60.25 days = 0.511
Since each half-life results in a decrease to half of the initial amount, we can calculate the percentage of the sample remaining by raising 0.5 to the power of the number of half-lives:
Percentage remaining = (0.5)^0.511 * 100 = 70.3%