In an ancient cave, charcoal fragments have a decay rate of 1.69 disintegrations per minute per gram of carbon 14. In comparison the decay rate for living tissue is 13.5 disintegrations per minute per gram. Find the age of the carbon fragments..

let T be the time the charcoal was formed and t=0 be the present day.

Can someone explain why N'(T)/N(0) = N(T)/N(0)

additional info: half life is 5568 years and assuming exponential decay so N'=-kN and N(T)=n0*exp(-kT)