time \(t = 46\) years

Exponential behavour of the number of undecayed nuclei

\(\displaystyle{N}={N}_{{o}}{e}^{{-\lambda}}{t}\)

\(\displaystyle{\frac{{{N}}}{{{N}_{{o}}}}}={e}^{{-\lambda}}{t}\)

half life of Sr is 28.9 years

decay constant \(\displaystyle\lambda={\frac{{{0.693}}}{{{t}^{{\frac{{1}}{{2}}}}}}}\)

\(=\frac{0.693}{28.9}\)

\(=0.0239\)

\(\displaystyle{\frac{{{N}}}{{{N}_{{o}}}}}={e}^{{-{0.0239}\cdot{46}}}\)

\(\displaystyle={0.3331}\)

\(=33.31\%\)

time \(t = 59\) years

\(\displaystyle{\frac{{{N}}}{{{N}_{{o}}}}}={e}^{{-{0.0239}\cdot{59}}}\)

\(\displaystyle={0.2441}\)

\(=24.41\%\)

time \(t=70\) years

\(\displaystyle{\frac{{{N}}}{{{N}_{{o}}}}}={e}^{{-{0.0239}\cdot{70}}}\)

\(=0.1877\)

\(=18.77\%\)