One method of dating rocks uses the decay of ⁴⁰K to ⁴⁰Ar with a half-life of 1.26x10⁹ yr. Most of the time, ⁴⁰K decays to 40Ca, and 11% of the time it decays to 40Ar. Initially, when the minerals in the rock form, there is very little argon included because argon is an inert noble gas. Potassium is abundant in nature, and most rocks have trace amounts of ⁴⁰K. To find the age of a rock, a sample is crushed into a fine powder and the released argon is carefully measured. The amount of ⁴⁰K is then extracted from the same sample and precisely measured. 

(a) A rock sample taken from atop a canyon wall is found to have one argon atom for every 52 atoms of ⁴⁰K. Approximately how old is the rock from the top strata? 

(b) Another sample of rock is taken from the bottom of the canyon at the base of this cliff wall. This sample is found to have one argon atom to every ten ⁴⁰K atoms. How much older is the rock at the canyon bottom than the rock at the top?