Mathematics: Amammoth bone is found to contain roughly 5% of the isotope c-14. living elephant bones commonly contain about 40% c-14. given that c-14 has a half-life of 5,730 years, how long ago did this mammoth die? show your work. (hint: no complex math is needed to solve this problem)

14 -w-Step-by-step explanation:...

Amammoth bone is found to contain roughly 5% of

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AliceYT

04.01.2022

Mathematics

$\large \boxed{\text{17 190 yr ago}}$

Step-by-step explanation

The amount of C-14 has declined from 40 % to 5 % of the original, that is, to ⅛ of the original amount.

The half-life of C-14 (5730 yr) is the time it takes for half of the isotope to decay.

We can make a table of the amount remaining after each successive half-life.

$\begin{array}{ccc}\textbf{Number of} && \textbf{Fraction} \\\textbf{half-lives} & \textbf{Years} & \textbf{remaining} \\0 &0 & 1 \\1 &5730 &\frac{1}{2 } \\\\2 &11460 &\frac{1}{4 } \\\\3 &17190 &\frac{1}{8} \\\\4 & 22920& \frac{1}{16} \\\end{array}\\\text{We see that the fraction of C-14 is reduced to $\frac{1}{8}$ after three half-lives.}\\\text{The mammoth died $\large \boxed{\textbf{17 190 yr ago}}$}$

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Amammoth bone is found to contain roughly 5% of the isotope c-14. living elephant bones commonly contain about 40% c-14. given that c-14 has a half-life of 5,730 years, how long ago did this mammoth die? show your work. (hint: no complex math is needed to solve this problem)

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