This is called the half-life of the sample.
The most important thing to remember is that while half the sample decays after one half-life, the whole sample does not entirely decay after two half-lives. After the first half-life, the remaining half of the sample in effect acts as its own sample, independent of the decay product(s) intermingled with it. Half of this half decays during the second half-life.
So after two half-lives one-fourth of the sample remains, then one-eighth after three half-lives, and so on in a decreasing geometric progression, called exponential decay. In the case of carbon dating our instruments are sensitive enough to follow this decay for at least eight half-lives.