Answer:
13282.3 years
Explanation:
The C-14 decays exponentially:
[tex]\frac{dN}{dt} =λ*N[/tex]
The solution for this equation is
[tex]N= N_{o}*e^{- λt}[/tex]
Where:
No = atom number of C-14 in t=0
N = atom number of C-14 now
I= radioactive decay constant
clearing t this equation we get:
[tex]t=-\frac{1}{ λ}*ln\frac{N}{N_{o}}[/tex]
The term 1/I is called half-life and the value for C-14 is 8252 years.
N for this exercise is 0.2No
[tex] t= -8033 * ln \frac{0.2N_{o} }{N_{o}}[/tex]
t = 13282.3 years
