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 this sample.

In your word document, paste the Excel table you made to come up with your answer.

Answer / Step-by-step explanation:

From the narrative in the question, we have come to understand that what we are being asked to solve for is the time (t).

but before that, we need to understand what half life means: Half life is the time it takes for half of a particle to decay from its initial size.

Now, recalling the formula for calculating the life time of a particle, we have:

N(t) = N₀ e ∧ ₋t/r

where

N(t) is the amount at time t

N₀ is the original amount

Therefore,

In ( N(t) / N₀ ) = - t / r

Now, if we go forward to making time (t) the subject of formula,

we have,

t = -r In (N(t) / N₀)

= Now, if we insert the values properly, we have:

we will arrive at 96%