One-eighth of an original radioactive sample will remain at the end of half-lives

One-eighth of an original radioactive sample will remain at the end of THREE half-lives

Explanation:

As we know that half life is defined as the time after which a radioactive nuclei will remain half in the number as we compare it with the initial amount present in the sample.

So here let say initially sample contains N number of radioactive atoms

so after one half life we will have "N/2" present in that sample

after 2nd half life the number of nuclei again becomes half of the remaining

now after 3rd half life we can say

so here correct answer will be

One-eighth of an original radioactive sample will remain at the end of THREE half-lives

6 cos 34, 6 sin 34 trig