# Do carbon dating equations

Now, take the logarithm of both sides to get $$-0.693 = -5700k,$$ from which we can derive $$k \approx 1.22 \cdot 10^. If you're seeing this message, it means we're having trouble loading external resources on our website. The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope). The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000). A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. I do not get the -0.693 value, but perhaps my answer will help anyway. If we assume Carbon-14 decays continuously, then$$ 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.Figure 1: This gif shows the comparison in radioactivity between a sample, or unknown (green area) , a modern standard (dark blue) and a background (small red peaks) derived from beta decay. A radiocarbon measurement, termed a conventional radiocarbon age (or CRA) is obtained using a set of parameters outlined by Stuiver and Polach (1977), in the journal Radiocarbon.A time-independent level of C14 activity for the past is assumed in the measurement of a CRA.According to Stuiver and Polach (1977), all laboratories should report their results either directly related to NBS Oxalic acid or indirectly using a sub-standard which is related to it.It is vital for a radiocarbon laboratory to know the contribution to routine sample activity of non-sample radioactivity. This is the International Radiocarbon Dating Standard.