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

Answer 1

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

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:
`(A)/(A_(o))=0.19` (2)

Now,finding
`t` from (1):

`(A)/(A_(o))=e^(-0.0001211.t)` (3)

Applying natural logarithm on both sides:

`ln((A)/(A_(o)))=ln(e^(-0.0001211.t))` (4)

`ln(0.19)=-0.0001211.t` (5)

`t=(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