iodine-131 has a half-life of 8 days. what percent of a sample would remain after 24 days

we are finding the amount of the sample undecayed after 24 days.

Iodine-131 has a half life of 8 days 28 minutes and 48 seconds,

But we can ignore the 8 minutes and the seconds sine it is not up to a day.

 Therefore let us observe it this way

Half life is the time taken for half of the mass of a sample to disappear,

Given that

 iodine has a half life T_1/2 = 8 days.

 let us observe it in this way, after one half-life elapse 50% percent of its mass is given off, and 50% of the mass is left and it takes 8 days . After another half-life,  ½ of the remaining 50 percent is also gone , we are left with only 25 percent of the original mass and this after 16 days.

After two half-life 75% mass is lost we are left with 25% and it takes 16 days( 16 days) . Therefore after another half-life ½ of the remaining 25% which is 12.5% percent of the original mass is left and it will take 24 days( 16+8 days).

Therefore after 3 half life 75% + 12% =87.5% is lost and only 12.5% remains ,

Each half takes 8 days

 there 3 * 8 = 24days

 in a tabular form we can have

S/n	Number of half-life	Amount remaining	Amount decayed	Total	Number of days
1	One	50%	50%	100%	8 days
2	Two	25%	75%	100%	16 days
3	Three	12.5%	87.5%	100%	24. days

Therefore after 24 days,  12.5 % is left.