Answer:
[tex]t = 2927.031\,years[/tex]
Explanation:
The time constant of the carbon-14 is:
[tex]t_{1/2} = \tau\cdot \ln 2[/tex]
[tex]\tau = \frac{t_{1/2}}{\ln 2}[/tex]
[tex]\tau = \frac{5730\,yr}{\ln 2}[/tex]
[tex]\tau = 8266.642\,years[/tex]
The equation of the decayment of the mass of the isotope:
[tex]\frac{m(t)}{m_{o}} = e^{-\frac{t}{\tau} }[/tex]
[tex]0.60 = e^{-\frac{t}{5730\,yr} }[/tex]
[tex]\ln 0.60 = -\frac{t}{5730\,yr}[/tex]
[tex]t =-(5730\,yr)\cdot \ln 0.60[/tex]
[tex]t = 2927.031\,years[/tex]
