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A sample of a radioactive substance decayed to 90.5% of its original amount afte

ID: 2882103 • Letter: A

Question

A sample of a radioactive substance decayed to 90.5% of its original amount after a year. (Round your answers to two decimal places.) What is the half-life of the substance? How long would it take the sample to decay to 90% of its original amount? 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 64% 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.) A roast turkey is taken from an oven when its temperature has reached 185 degree F and is placed on a table in a room where the temperature is 75 degree F. (Round your answers to the nearest whole number.) If the temperature of the turkey is 150 degree F after half an hour, what is the temperature after 45 minutes? When will the turkey have cooled to 110 degree?

Explanation / Answer

21) 90.5%

f = 0.905^t

a) for half-life,

0.5 = 0.905^t
t = ln 0.5 / ln 0.905

t= 6.94395 years

b) decay to 90%

0.9 = 0.905^t
t = ln 0.9 / ln 0.905

t = 1.05550 years