The average half-life of C-14 is 5730 years.
If M is the mass of C-14 in a sample, we can find the exponent -bt: M/2=Me^(-bt):
0.5=e^-5730t, b=ln(0.5)/-5730=1.2×10⁻⁴ approx.
Therefore m=m₀e⁻⁰˙⁰⁰⁰¹²ᵗ, where m₀ is the original mass.
If m=m₀×8⁻¹⁴, then -14ln(8)=-0.00012t and t=14ln(8)/0.00012=243000 years approx.
This assumes that all the carbon was C-14.