Archeologists and geologists use half-life to date the age of organic objects in a process known as carbon dating. At the time of death organisms stop producing carbon 14.
Since half life is a constant, the ratio of carbon 14 to nitrogen 14 provides a measurement of the age of a sample.
After two half-lives, the mother substance will decay another 50%, leaving 25% mother and 75% daughter.
A third half-life will leave 12.5% of the mother and 87.5% daughter.
The detector, therefore, counts only the carbon-14 atoms within the sample.