In a radioactive sample, ${\mathrm{ }}_{19}^{40}\mathrm{K}$ nuclei either decay into stable ${\mathrm{ }}_{20}^{40}\mathrm{C}\mathrm{a}$ nuclei with decay constant $4.5\times {10}^{-10}$ per year or into stable ${\mathrm{ }}_{18}^{40}\mathrm{A}\mathrm{r}$ nuclei with decay constant $0.5\times {10}^{-10}$ per year. Given that in this sample all the stable ${\mathrm{ }}_{20}^{40}\mathrm{C}\mathrm{a}$ and ${\mathrm{ }}_{18}^{40}\mathrm{A}\mathrm{r}$ nuclei are produced by the ${\mathrm{ }}_{19}^{40}\mathrm{K}$ nuclei only. In time $\mathrm{t}\times {10}^9$ years, if the ratio of the sum of stable ${\mathrm{ }}_{20}^{40}\mathrm{C}\mathrm{a}$ and ${\mathrm{ }}_{18}^{40}\mathrm{A}\mathrm{r}$ nuclei to the radioactive ${\mathrm{ }}_{19}^{40}\mathrm{K}$ nuclei is $99,$ the value of t will be : [Given $\mathrm{l}\mathrm{n}\mathrm{ }10=2.3$ ]