The mathematical formula that is used to figure the age of the rock depends on the half-life of carbon-40 (the time it takes for half the potassium-40 in a given sample to decay). The half-live of potassium-40 is approximately 1.26 billion years (that is, 1.26x109 year | The mathematical formula that is used to figure the age of the rock depends on the half-life of carbon-40 (the time it takes for half the potassium-40 in a given sample to decay). The half-live of potassium-40 is approximately 1.26 billion years (that is, 1.26x109 year |