\(A = A _{0} e ^{-\lambda t_{2}}....(i)\)

\(\frac{ A }{5}= A _{0} e ^{-\lambda t_{2}}....(ii)\)

\(( i ) \div ( ii )\)

\(5= e ^{\lambda\left(t_{2}-t_{1}\right)}\)

\(\lambda=\frac{\ell n 5}{t_{2}-t_{1}}=\frac{1}{\tau}\)

\(\tau=\frac{t_{2}-t_{1}}{\ell n \cdot 5}\)