Scientists can determine the age of ancient objects by the method of radiocarbon

Question

Scientists can determine the age of ancient objects by the method ofradiocarbon 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 assimilates14C through food chains. When a plant or animal dies, it stops replacing its carbon and the amount of14C begins to decrease through radioactive decay. Therefore the level of radioactivity must also decay exponentially. A parchment fragment was discovered that had about71%as much14C radioactivity as does plant material on earth today. Estimate the age of the parchment. (Round your answer to the nearest whole number.)
yr

Explanation / Answer

remaining amout = 0.5^(t/h)

given half life = h = 5730 years.


0.71 = (1 / 2)^(t / 5730)

(t / 5730) log (1 / 2 ) = log (0.71)

t = 5730 log(0.71) / log(0.5)

t = 2831.244972647344556 years.

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