Hello, blenyo!

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.