assume that the global amount of radiocarbon is constant, and that decaying carbon-14 is continuously replaced in organisms when they are alive. however, once an organism dies, the amount of carbon-14 in it decreases continuously as it decays to nitrogen-14. a. the carbon in a buried peat bed has about 6% of the carbon-14 of modern shells. what is the age of the peat bed? explain.

t is the half-life of carbon-14, which is approximately 5,730 years.
R_0 is the initial ratio of carbon-14 to carbon-12 in the sample, which is approximately 0.01 in modern shells.
R is the current ratio of carbon-14 to carbon-12 in the sample, which is approximately 0.006 in the peat bed (6% of the carbon-14 of modern shells).

Plugging these values into the formula gives us:

Age = 5,730 years * ln(0.01/0.006)

Age = 5,730 years * 0.778

Age = 4,429 years

This method of dating, known as radiocarbon dating, is based on the fact that carbon-14 is continuously replaced in living organisms, but once an organism dies, the amount of carbon-14 in it decreases continuously as it decays to nitrogen-14. By measuring the ratio of carbon-14 to carbon-12 in a sample, it is possible to determine how long it has been since the organism died, assuming that the global amount of radiocarbon is constant.

Learn more about radiocarbon dating here:

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