Suppose you find a rock that contains 10 micrograms of radioactive potassium-40, which has a half-life of 1.25 billion years. By measuring the amount of its decay product (argon-40) present in the rock, you conclude that there must have been 80 micrograms of potassium-40 when the rock solidified. How old is the rock?
The current 10 micrograms of potassium-40 is 1/8 of the original 80 grams, which means the amount of potassium-40 has declined by a factor of 8. Therefore, three half-lives have passed (since 23 = 8) and the rock is 3x1.25 = 3.75 billion years old.