Ancient paintings were found on cave walls in South America. The Carbon-14 in the paintings was measured and was found to be 19% of the orig

Question

Ancient paintings were found on cave walls in South America. The Carbon-14 in the paintings was measured and was found to be 19% of the original weight. How old were the paintings?

A. 3,839
B. 9,239
C. 13,839
D. 19,239

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Isabelle 2 weeks 2021-09-10T22:20:22+00:00 1 Answer 0

Answers ( )

    0
    2021-09-10T22:21:36+00:00

    Answer: C. 13,839 (the answer is not among the given options, however the result is near this value)

    Step-by-step explanation:

    The exponential decay model for Carbon-
    14 is given by the followig formula:

    A=A_{o}e^{-0.0001211.t}  (1)

    Where:

    A is the final amount of Carbon-
    14  

    A_{o}= is the initial amount of Carbon-
    14

    t is the time elapsed (the value we want to find)

    On the other hand, we are told the current amount of Carbon-14 A  is 19\%=0.19, assuming the initial amount of Carbon-14 A_{o}= is  100\%:

    A=0.19A_{o} (2)

    This means: \frac{A}{A_{o}}=0.19 (2)

    Now,finding t from (1):

    \frac{A}{A_{o}}=e^{-0.0001211.t}  (3)

    Applying natural logarithm on both sides:

    ln(\frac{A}{A_{o}})=ln(e^{-0.0001211.t})  (4)

    ln(0.19)=-0.0001211.t  (5)

    t=\frac{ln(0.19)}{-0.0001211}  (6)

    Finally:

    t=13713.717years  This is the age of the paintings and the option that is nearest to this value is C. 13839 years

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