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Over time there is a gradual decrease in the amount of Carbon-14 and the ratio of Carbon-14 atoms to other Carbon atoms declines. Therefore half of the Carbon-14 has decayed after 5730 years.
Half of the remaining Carbon-14 then decays over the next 5730 years leaving one fourth of the original amount.
We cannot predict exactly which atom will decay at a certain time but we can estimate, using the half-life, how many will decay over a period of time.
The half-life of a substance can be found by measuring the count-rate of the substance with a Geiger-Muller tube over a period of time.
By measuring the ratio of Carbon-14 in a sample and comparing it to the amount in a recently deceased sample its date can be determined.