Now, take the logarithm of both sides to get $$-0.693 = -5700k,$$ from which we can derive $$k \approx 1.22 \cdot 10^.$$ So either the answer is that ridiculously big number (9.17e7) or 30,476 years, being calculated with the equation I provided and the first equation in your answer, respectively.

Carbon dating has given archeologists a more accurate method by which they can determine the age of ancient artifacts.

Libby invented carbon dating for which he received the Nobel Prize in chemistry in 1960.

When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years.

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.

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 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.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.The Oxalic acid standard was made from a crop of 1955 sugar beet. The isotopic ratio of HOx I is -19.3 per mille with respect to (wrt) the PBD standard belemnite (Mann, 1983). T designation SRM 4990 C) was made from a crop of 1977 French beet molasses.

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