Determine the total time that must elapse until only 1/16 of an original sample of th-234 remains unchanged.

Answer is: the total time that must elapse until only 1/16 of an original sample of Th-234 remains unchanged is 96.4 days.

Half-life of thorium-234 isotope is 24.1 days.
After first half-life there is 1/2 of an original  sample.
After second half-life there is 1/4 of an original sample.
After third half-life there is 1/8 of an original sample.
After fourth half-life there is 1/16 of an original  sample, so after four half lifes:
 4 · 24.1 days = 96.4 days.

Ais the correct answer