Mass spectrometric analysis of potassium and argon atoms in a Moon rock sample shows that the ratio of the number of (stable) ${ }^{40} Ar$ atoms present to the number of (radioactive) ${ }^{40} K$ atoms is $10.3$. Assume that all the argon atoms were produced by the decay of potassium atoms, with a half-life of $1.25 \times 10^{9} yr$. How old is the rock?