# Carbon dating formula math

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^.If possible, the ink should be tested, since a recent forgery would use recently-made ink.The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope).The older a sample is, the less (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.The idea behind radiocarbon dating is straightforward, but years of work were required to develop the technique to the point where accurate dates could be obtained.Other useful radioisotopes for radioactive dating include Uranium -235 (half-life = 704 million years), Uranium -238 (half-life = 4.5 billion years), Thorium-232 (half-life = 14 billion years) and Rubidium-87 (half-life = 49 billion years).

A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. I do not get the $-0.693$ value, but perhaps my answer will help anyway.

­ ­As soon as a living organism dies, it stops taking in new carbon.

The ratio of carbon-12 to carbon-14 at the moment of death is the same as every other living thing, but the carbon-14 decays and is not replaced.

However, I note that there is no beginning or ending amount given.

How am I supposed to figure out what the decay constant is?

The development of radiocarbon dating has had a profound impact on archaeology.