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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.The kerosene is purified by removing pollutants, using a clay filter.Suppose the clay is in a pipe and as the kerosene flows through the pipe, every foot of clay removes 20% of the pollutants, leaving 80%.

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This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.

The halflife of carbon 14 is 5730 ± 30 years, and the method of dating lies in trying to determine how much carbon 14 (the radioactive isotope of carbon) is present in the artifact and comparing it to levels currently present in the atmosphere.

Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.

For radiocarbon dating to be possible, the material must once have been part of a living organism.

This means that things like stone, metal and pottery cannot usually be directly dated by this means unless there is some organic material embedded or left as a residue.

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