A wooden artifact from an ancient tomb contains 70 of the ca

A wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number

Solution

Using the half life formula,

Amount after t years=(1/2)^(t/5730), we get

0.70=(1/2)^(t/5730) , take natural log both sides to get

ln(0.7)= ln[ (0.5)^(t/5730)]

ln(0.7)= [t*ln(0.5)] / 5730

t=[5730*ln(0.7)] / ln(0.5)

t=2948.504

t= 2949 years.

Hence the artifact was made about 2949 years ago.