Carbon-14 is a radioactive isotope of carbon which has a half-life of about 5600 years.
Let be the nearly constant ratio of corbon-12 found in the atmosphere.
Let be the ratio of carbon-14 to carbon-12 found in an observed specimen.
It has been shown for carbon-14 dating of objects that: .R = re^[(t ln4)/5600]
. . where is the age of the object in years.
Suppose a specimen has been found in which r = 0.2R
Find the age of the specimen.
We have: .R/r = e^[(t ln4)/5600]
We are given: .r = 0.2R . → . R/r = 5
Hence: .e^[(t ln4)/5600] .= .5
. a . . . . . . .(t ln4)/5600 .= .ln5
. n . . . . . . . . . . . . . . t .= .(5600 ln5)/(ln4)
Therefore: .t .≈ .6501.4 years.