2022 FMSS AM S4 P1 Q2

Clarification: \(P\) denotes the fraction remaining, and \(100P\) is the percentage remaining. Use \(P=0.50\) for 50% and \(P=0.34\) for 34%.

It was found that the fraction of the initial carbon-14, \(P\), contained in the bones of an animal \(n\) years after it has died is given by \(P = 2^{-kn}\), where \(k\) is a positive constant. The percentage of carbon-14 contained in the bones after the animal has been dead for 7200 years was 50%. How long, to the nearest year, was the animal dead if the percentage of carbon-14 found in the bones was only 34%?[4]