In order to understand the prehistory of the Hawaiian island of Lana'i better, anthropologists Maria Sweeney, Melinda Allen, and Boyd Dixon used radiocarbon dating on charcoal found in an ancient dwelling site, the Kaunolu Village National Historic Landmark, the largest archeological complex on the island. In one of their samples, they found that approximately 94% of the original carbon 14 remained. Using the fact that Carbon 14 decays by 1.202% every 100 years, determine the approximate age of the this sample.

Question

unklerhaukus · Answer

We are solving for time t
tau is the half-life (same units as t)
N(t) is amount at time t
N_0 is original amount 

$$N(t) = N_0e^{\frac{- t}{\tau}}$$
$$\frac{N(t)}{N_0} = e^{\frac{- t}{\tau}}$$
$$\ln(\frac{N(t)}{N_0})=\frac{-t}{\tau}$$
$$t=-\tau\ln(\frac{N(t)}{N_0})=$$

unklerhaukus · Answer

$$\frac{N(t)}{N_0}=96\%$$

anonymous · Answer

I have not reached that level of math before, but I did figure out the answer through excel. Thank you very much for trying to help though!

unklerhaukus · Answer

this might not be the way the questioner intended  you to answer