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Living plants and animals all contain the chemical element carbon. A certain percentage of that carbon is radioactive, and scientists believe that the parentage has remained constant for thousands of years. Radioactive carbon decays, so that when an animal dies, a tiny bit of the radioactive carbon is lost each year. It is known that the amount of radioactive carbon that remains in a fossil at the end of a year is approximately 0.99988 of the amount that was present at the beginning. Thus, the following dynamical system describes radioactive carbon
decay in a fossil:
This system behaves exactly like the compound interest situation (except the amount or radioactive carbon is decreasing), so it is easy to see that after k years, the amount of radioactive carbon in the fossil will be
Carbon dating. A fossilized bone is found that contains 90% of the original radioactive carbon that was present. To the nearest 100 years, how old is the bone?
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