Geologist know that potassium 40 decays to argon 40, with a half life of 1.3 billion years. analysis of a hypothetical sample of granite reveals that 75 percent of the potassium 40 atoms have decyaed to form argon 40. what is the age of the sample of granite

First let us calculate for the rate constant k from the formula:

k = ln(2) / t0.5

where t0.5 is the half life

k = ln(2) / 1.3x10^9 years

k = 5.33x10^-10 years-1

Then we use the formula:

A/Ao = e^-kt

where A/Ao is the amount remaining = 25% = 0.25, t is time

Rearranging to get t:

t = ln(A/Ao) / -k

t = ln(0.25) / (-5.33x10^-10 years-1)

t = 2.6x10^9 years