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## 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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Math
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2021-09-10T22:20:22+00:00
2021-09-10T22:20:22+00:00 1 Answer
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## Answers ( )

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:

(1)Where:is the

final amount of Carbon-14

is the

initial amount of Carbon-14

is the

time elapsed(the value we want to find)On the other hand, we are told the current amount of Carbon-14 is , assuming the initial amount of Carbon-14 is :

(2)This means:

(2)Now,finding from

(1):(3)Applying natural logarithm on both sides:(4)(5)(6)Finally:This is the age of the paintings and the option that is nearest to this value is C. 13839 years