Let Q(t) be the amount of the radioactive substance at time t and A be the amount of initial radioactive substance. Since decay of the amount of radioactive substance is exponential, the function Q(t) has the following form:

Q(t) = Q₀e^kt

for t=0›A= Q₀   then Q(10)=0,95A=A.e^k10

ln 0,95=10k and k=(ln0,95)/10

To find the half-life of this radioactive material we should solve the equation;

0,5A=A.e^{((ln0,95)/10).t}

ln0.5=(ln0,95/10)).t ›135,13