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Answer :
To determine the fraction of C-14 remaining in the plank compared to a living organism: the age of the plank is approximately 1508 years old.
fraction remaining = (activity of sample) / (activity of living organism)
fraction remaining = 38.8 / 47.5
fraction remaining = 0.817
Next, we can use the half-life of C-14 to calculate the number of half-lives that have passed:
number of half-lives = (ln fraction remaining) / (ln 0.5)
number of half-lives = (ln 0.817) / (ln 0.5)
number of half-lives = 0.263
Finally, we can use the half-life and number of half-lives to calculate the age of the plank:
age = (number of half-lives) x (half-life)
age = 0.263 x 5730
age = 1508 years
Therefore, the age of the plank is approximately 1508 years old.
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