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

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