Answer:
C. 11400 years.
Explanation:
The time constant of the isotope is:
[tex]\tau = \frac{5730\,yr}{\ln 2}[/tex]
[tex]\tau = 8266.643\,yr[/tex]
The decay of the isotope is described by the following model:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
[tex]-\frac{t}{\tau} = \ln \frac{m(t)}{m_{o}}[/tex]
[tex]t = -\tau \cdot \ln \frac{m(t)}{m_{o}}[/tex]
[tex]t = -(8266.643\,yr)\cdot \ln \left(\frac{1}{4} \right)[/tex]
[tex]t \approx 11460.001\,yr[/tex]
The right answer is C.
