One specific example of exponential decay is purified kerosene, used for jet fuel.The kerosene is purified by removing pollutants, using a clay filter.
SAL: The notion of a half-life is useful, if we're dealing with increments of time that are multiples of a half-life.
For example, where time equals zero, we have 100% of our substance.
Then after time equals one half-life, we'd have 50% of our substance.
The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope).
The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000).