The the rate of decay of the element I-131 decreases from 10 microcuries to 5 microcuries in 10 days. Curie is the non-SI unit of radioactivity and is equal to 3.7*10^10 decays per second.
Half life of an element undergoing decay is the time taken for the initial amount of a substance to decrease to half the value. As the amount of a substance decreases so does the rate of decays per second. In the case of I-131 after 10 days the number of decays after ten days has reduced to half the number of decays taking place initially.
Else, use the relation N(t) = N0*(1/2)^(t/th) where th is the half life.
5 = 10*(1/2)^(10/th)
=> 1/2 = (1/2)^(10/th)
=> 10/th = 1
=> th = 1
The half life of I-131 is 10 days.