## 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

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

1. 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