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After 920 = 17190 2 \times 2865$ years, the reasoning in the previous paragraph shows that there will be $$ \left(\frac\right) r^2 $$ micrograms of Carbon 14.According to the table, this quantity is also $\frac$ of a microgram and so we find $$ \left(\frac\right) r^2 = \frac. Once the rate $r$ has been determined, the amount of Carbon 14 remaining after 055$ years is calculated as above and found to be about $\frac$ or a little less than /10$ of a microgram.Libby and coworkers, and it has provided a way to determine the ages of different materials in archeology, geology, geophysics, and other branches of science.

As you learned in the previous page, carbon dating uses the half-life of Carbon-14 to find the approximate age of certain objects that are 40,000 years old or younger.

In the following section we are going to go more in-depth about carbon dating in order to help you get a better understanding of how it works.

The carbon-14 atoms combine with oxygen to form carbon dioxide, which plants absorb naturally and incorporate into plant fibers by photosynthesis.

Animals and people take in carbon-14 by eating the plants.

By measuring the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of the artifact.

Carbon 14 is a common form of carbon which decays exponentially over time.

An essential characteristic of exponential functions is that their values change by equal factors over equal intervals, that is, if $f(x)$ is an exponential function and $b$ a fixed real number, then the quotient $$ \frac $$ always takes the same value, that is, it does not depend on the real number $x_0$.

This exploratory task requires the student to use this property of exponential functions in order to estimate how much Carbon 14 remains in a preserved plant after different amounts of time.

Each time this calculation is iterated, the estimated period of time for when one microgram of Carbon 14 remains is cut in half.

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