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This half life is a relatively small number, which means that carbon 14 dating is not particularly helpful for very recent deaths and deaths more than 50,000 years ago.

In the case of radiocarbon dating, the half-life of carbon 14 is 5,730 years.

If we assume Carbon-14 decays continuously, then $$C(t) = C_0e^,$$ where $C_0$ is the initial size of the sample. Since it takes 5,700 years for a sample to decay to half its size, we know $$\frac C_0 = C_0e^,$$ which means $$\frac = e^,$$ so the value of $C_0$ is irrelevant.

Now, take the logarithm of both sides to get $$-0.693 = -5700k,$$ from which we can derive  k \approx 1.22 \cdot 10^.

For example, there is a radioactive form of potassium (potassium-40) that decays into argon (argon-40).

The unstable potassium isotope is called the parent while the argon product is called the daughter.