The half-life for radioactive decay of `14_{C}` is 5730 years. An archaeological artifact containing wood had only 80 % of the `14_{C}`found in a living tree. Estimate the age of the sample.

Explanation

`[(A)]_(0)=100 ,[(A)]=80`
`(k)=(0.693)((t)_(2))=(0.693)(5730) years`

`t=(2.303)((k)) log ([(A)]_(0))([(A)])=(2.303 * 5730)(0.693) log ([100])([80])`
`= (2.303 * 5730)(0.693) log 1.25=1845 year`