Suppose you find a rock originally made of potassium-40, half of which decays into argon-40 every 1.25 billion years. You open the rock and find 31 atoms of argon-40 for every atom of potassium-40. How long ago did the rock form?

We see that in 1 rock, there are 31 atoms of Argon and 1 atom of Potassium so the relative concentration of Potassium is:

1 / 32

or can be written as:

1 / 2^5

So this means that 5 half-lives have passed.

So the years are:

years passed = 5 * 1.25 billion years = 6.25 billion years