The amount of ^{14}C in an old, isolated sample of vegetation is 0.809 that expected from a present day sample with an equivalent carbon content. Calculate the age of the old sample in years.

The half life of C14 is 5730 years.

Assuming the age of this sample is t.

Then (1/2)^(t/5730)=0.809

t/5730=log 0.809/log 0.5=0.306

t=5730x0.306=1753 years

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