The ratio of carbon 14 to carbon 12 of the piece of wood was R= 1/(8^14)
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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.

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