Activity of a sample of a radio active material A1, at a time t1 and A2 at a time t2. If mean life is T then
A1t1=A2t2
T=A2-A1t2-t1
A1A2=et2-t1T
A2=A1t1Tt2
A1=λN0e-λt1 and A2 =λN0e-λt2
dividing A1A2=e-λt1e-λt2=et2-t1λ=et2-t1T T=1λ