Carbon-14 has a half-life of 5,730 ± 40 years— during the succeeding 5,730 years.
Because carbon-14 decays at this constant rate, an estimate of the date at which an organism died can be made by measuring the amount of its residual radiocarbon.
Since that decays and the other $\ce$-isotopes don't, over the years, the percentage of $^\ce$ is getting lower and lower at a constant rate (you can calculate that rate with the half-time of $^\ce$).
Now when you measure the relative amount of $^\ce$ in a skeleton, you know since when it hasn't eaten anymore, so you know how old it is.
Since carbon is fundamental to life, occurring along with hydrogen in all organic compounds, the detection of such an isotope might form the basis for a method to establish the age of ancient materials.
Libby, a Professor of Chemistry at the University of Chicago, predicted that a radioactive isotope of carbon, known as carbon-14, would be found to occur in nature.
During the lifetime of an organism, the amount of c14 in the tissues remains at an equilibrium since the loss (through radioactive decay) is balanced by the gain (through uptake via photosynthesis or consumption of organically fixed carbon).
However, when the organism dies, the amount of c14 declines such that the longer the time since death the lower the levels of c14 in organic tissue.
We know that it is older than Christendom, but whether by a couple of years or a couple of centuries, or even by more than a millenium, we can do no more than guess." [Rasmus Nyerup, (Danish antiquarian), 1802 (in Trigger, 19)].
This is not true for zeroth- and second-order reactions.
The half-life of a first-order reaction is independent of the concentration of the reactants.
If two reactions have the same order, the faster reaction will have a shorter half-life, and the slower reaction will have a longer half-life.
The half-life of a first-order reaction under a given set of reaction conditions is a constant.