If the activity of a certain mass of carbon from plant or animal that is just active (before it dies) is A0 and that from the same mass of carbon from the sample to be dated is A,

Then

OR ALTERNATIVE WE CAN DERIVE THE EQUATIONS AS FOLLOWS

According to the  law of radioactivity, the rate of decay is proportional to the original number

Note replace H with λ and replace v in the above equation with  proportionality constant α

TAKING THE reciprocal from both side we have

 But let D =