Let’s say that I can make a dozen cookies in 2 hours.I am just learning the recipe so it takes me more time to look back and forth and double check.Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon.
And this isn’t really an assumption as the decay rates have been tested in the laboratory for a hundred years or so, we have an example of a natural nuclear reactor where we can measure the various products and determine the decay rates (and the fine structure constant), and we can observe the past by looking deep into the past of the universe. The sigh isn’t for the effort of writing, it’s for the effort of finding all the references.
One specific example of exponential decay is purified kerosene, used for jet fuel.
The kerosene is purified by removing pollutants, using a clay filter.
When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon 14.
Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.