What percentage of an original sample of iodine-131 will remain after 64 days if iodine-131 has a half-life of 8 days?

First, determine the number of half-lives that will occur over a 64-day period. Do this by dividing the 64-day period by the 8-day half-life.
64 ÷ 8 = 8
This tells us that there will be 8 half-lives during this 64 day period. The half-life of a substance is the time it takes for that substance to decay. After each half-life, half of the starting amount will have decayed. In this case, every 8 days, half of the amount of iodine-131 decays. Since this problem doesn’t give us a starting amount and instead, asks us to find the percentage, we can start by plugging in 100g as the starting amount. This way, the ending amount will automatically give us the percentage that’s left, because it is already out of 100. For each half-life, we divide the starting amount in half, like this:

Half-life: 1
100 → 50

Half-life: 2
50 → 25

Half-life: 3
25 → 12.5

Half-life: 4
12.5 → 6.25

Half-life: 5
6.25 → 3.125

Half-life: 6
3.125 → 1.5625

Half-life: 7
1.5625 → 0.78125

Half-life: 8
0.78125 → 0.390625

The ending amount is 0.39g out of 100g that we started with. Therefore, the remaining amount after 8 half-lives (64 days) is 0.39% of the starting amount.