Radioactive decay is a random process at the level of individual atoms, but entirely predictable in bulk. The half-life is the time for half of any quantity to decay, and it is the same regardless of how much you started with.
Nothing ever fully decays
Each half-life removes half of what remains, so the quantity approaches zero without reaching it. After ten half-lives about 0.1% is left; after twenty, one part in a million. This is why waste storage timescales are usually quoted as ten or twenty half-lives rather than as a point of complete disappearance.
Half-life is unaffected by conditions
Temperature, pressure and chemical state have essentially no effect, because decay is a nuclear process and chemistry happens in the electron shells. This is what makes radiometric dating reliable and why a sample cannot be made to decay faster.
Dating
Carbon-14 has a half-life of 5730 years, which suits archaeological timescales up to roughly 50,000 years. Beyond that too little remains to measure and longer-lived isotopes are used: potassium-40 at 1.25 billion years and uranium-238 at 4.5 billion years are the standard tools for dating rocks.
The same maths elsewhere
Drug elimination from the bloodstream, capacitor discharge and the cooling of a hot object all follow the identical exponential form. Only the constant changes.