The technique known as potassium-argon dating is used to date old lava flows. The potassium isotope ⁴⁰K has a 1.28 billion year half-life and is naturally present at very low levels. ⁴⁰K decays by two routes: 89% undergo beta-minus decay into ⁴⁰Ca while 11% undergo electron capture to become ⁴⁰Ar. Argon is a gas, and there is no argon in flowing lava because the gas escapes. Once the lava solidifies, any argon produced in the decay of ⁴⁰K is trapped inside and cannot escape. A geologist brings you a piece of solidified lava in which you find the ⁴⁰Ar/⁴⁰K ratio to be 0.013. What is the age of the rock?