A radioactive isotope${ }^{40}\mathrm{K}$ With a half-life of $1.26\times {10}^9$ years, decay to ${}_{ }{}^{40}Ar$ A sample of rock from the moon was found to contain both element $\mathrm{K}$and $\mathrm{Ar}$and they are in the ratio 1 : 7. What is the age of the rock? (Neglect decay of ${ }^{40}\mathrm{K}{\text{ to }}^{40}\mathrm{Ca}$)