Scientist can determine the age of ancient objects by a method called radiocarbo

Question

Scientist can determine the age of ancient objects by a method called radiocarbon dating. The bombardment of the upper atmosphere by cosmic rays converts nitrogen to a radioactive isotope of carbon, 14C, with a half-life of about 5730 years. Vegetation absorbs carbon dioxide through the atmosphere and animal life assimilates 14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of 14C begins to decrease through radioactive decay. Therefore, the level of radioactivity must also decay exponentially.
A parchment fragment was discovered that had about 74% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment.

Explanation / Answer

fraction remaining f = 0.5^(t/h) where h is the half-life 0.64 = 0.5^(t/5730) t = 5730*ln 0.64 /ln 0.5 = 3689 years

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