7. 0/1 pointsI Previous Answers SCalcET8 3.8.011 My Notes Ask Your Teact Scienti

Question

7. 0/1 pointsI Previous Answers SCalcET8 3.8.011 My Notes Ask Your Teact 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 75% as much 14C radioactivity as does plant material on Earth today. Estimate the age of the parchment. Round your answer to the nearest hundred years.) 2489.3 x yr Need Help? Read Watch It Talk to a Tutor

Explanation / Answer

general decay equation is A(t)=Aoe-kt, where initial amount A(0)=Ao

at halflife amount remaining,A(t)=(1/2)Ao

=>Aoe-k*5730=(1/2)Ao

=>ek*5730=2

=>5730k=ln(2)

=>k=(1/5730)ln(2)

=>A(t)=Aoe-((1/5730)ln(2))t

when 75% is remaining, A(t)= 0.75Ao

=>Aoe-((1/5730)ln(2))t= 0.75Ao

=>e-((1/5730)ln(2))t= 0.75

=>e((1/5730)ln(2))t= 4/3

=>((1/5730)ln(2))t= ln(4/3)

=>t= (5730ln(4/3))/ln(2)

=>t=2378.164870867775080270075851179

nearest hundered years => t =2400

therefore parchment fragment is  2400 years old

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