This is consistent with the assumption that each decay event is independent and its chance does not vary over time.
The solution is: where is the half-life of the element, is the time expired since the sample contained the initial number atoms of the nuclide, and is the remaining amount of the nuclide.
YEC biblical literalists are necessarily bound to the dogmatic religions conclusion that the Earth is of a certain age based on a particular literal interpretation of the Genesis creation myth.
We can measure directly, for example by using a radiation detector, and obtain a good estimate of by analyzing the chemical composition of the sample.
The half-life , specific to each nuclide, can be accurately measured on a pure sample, and is known to be independent of the chemical composition of the sample, temperature and pressure.
Carbon dating works on organic matter, all of which contains carbon.
However it is less useful for dating metal or other inorganic objects.