Question

A hiker in Africa discovers a skull that contains 7% of its original amount of C-14
find the age of the skull to the nearest year

Answer 1

\(\color{#0cbb34}{\text{Originally Posted by}}\) @reese
A hiker in Africa discovers a skull that contains 7% of its original amount of C-14
find the age of the skull to the nearest year
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 2

For exponential decay, with decay constant \(k\):

\(C = C_o e^{- k t}\)

For C-14 half life \(\tau (\approx 5730 \text{ years})\), we have :

\(\dfrac{1}{2} = e^{- k \tau} \implies k = \dfrac{\ln 2}{\tau}\)

For \(C = C_o \times 0.07\), we are solving:


\(0.07 = \exp\left( - \dfrac{\ln 2}{5730} t\right) \implies t = 21, 983\).... "to the nearest year".....

Closed, so no rules broken ;)