Question

Carbon-14 has a half-life of 5,730 years. A fossil is found that has 28% of the carbon-14 found in a living sample. How old is the fossil? (Round your answer to the nearest year.)

Answer 1

carbon-14 has half-life 5730 years

let after t years the fossil has 28% carbon-14

let the carbon-14 decay function is where P_o is the initial amount , k is the decay constant & t is in years

thus  

=>  

=>  

thus after 10523 years the fossil would have 28% carbon-14