We use the exponential decay formula to solve for the percentage of atoms in a sample of Plutonium-238 will remain radioactive after 263.1 years.
We are given with a half-life of 87.7 years and so, we can get the decay constant:
k = ln 2 / 87.7
k = 0.0079
A/A0 = exp(-kt)
A/A0 = exp (-0.0079(263.1))
A/A0 = 0.125
or
12.5%