Answer:
6163.2 years
Step-by-step explanation:
The formula we use for evaluating the C 14 decay is
[tex]A_t=A_0e^{-kt}[/tex]
Where
[tex]A_t[/tex]=Amount of C 14 after âtâ year
[tex]A_0[/tex]= Initial Amount
t= No. of years
k=constant
In our problem we are given that [tex]A_t[/tex] is 54% that is if [tex]A_0=1[/tex] , [tex]A_t=0.54[/tex]
Also , k=0.0001
We have to find t=?
Let us substitute these values in the formula
[tex]0.54=1* e^{-0.0001t}[/tex]
Taking log on both sides to the base 10 we get
[tex]log 0.54=log e^{-0.0001t}[/tex]
[tex]-0.267606 = -0.0001t*log e[/tex]
[tex]-0.267606 = -0.0001t*0.4342[/tex]
[tex]t=\frac{-0.267606}{-0.0001*0.4342}[/tex]
[tex]t=6163.20[/tex]
t=6163.20 years
