Given, half life of a certain radioactive element = 800 years.
Amount of substance remaining at time t = 12.5%
Lets consider the initial amount of the radioactive substance = 100%
Using the half life equation:
A = A₀(1/2)^t/t₁/₂
where A₀ is the amount of radioactive substance at time zero and A is the amount of radioactive substance at time t, and t₁/₂ is the half-life of the radioactive substance.
Plugging the given data into the half life equation we have,
12.5 = 100 . (1/2)^t/800
12.5/100 = (1/2)^t/800
0.125 = (0.5)^t/800
(0.5)^3 = (0.5)^t/800
3 = t/800
t = 2400 years
Thus the object is 2400 years old.