How long will it take for 3/4 of the sample of 131 iodine that has half-life of 8.1 days?
Since you didn't specify whether 3/4 of the sample remains or undergoes decay, I'll show you both cases.
Here's the equation for exponential decay used in nuclear half-life calculations
First case - 3/4 of the sample undergoes radioactive decay.
If 3/4 of the sample undergoes radioactive decay, you wil be left with 1/4 of the original sample. This means that
This implies that
It will take 16.2 days for 3/4 of your sample to undergo radioactive decay.
Second case - 3/4 of the sample remains, i.e. does not undergo radioactive decay.
The same principle applies in this case as well, only this time 1/4 of the sample will decay and 3/4 will remain. This means that
As a result,
It will take 3.36 days for 1/4 of the sample to undergo radioactive decay.