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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