How many hours will it take for only 1.5625 mg to remain

36 hours

Explanation:

Notice that you are given the actual table of how the isotope reduces , and it shows that for each period of 6 hours the isotope decays to half of the initial number.

EVery 6 hours, the reduction in number of mg of the isotope goes down in half'

100 mg, then 50 mg, then 25 mg, then 12.5 mg, then 6.25 mg, then 3.125 mg and finally (reaching 1.5625 mg

That was 6 periods of 6 hours each, which totals: 6 time 6 hours = 36 hours

well in order to answer this question you have to provide more information < 3

the answer is symmetrical : )