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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 original weight. How old were the paintings?

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

User Pensnarik
by
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1 Answer

4 votes

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

User Antew
by
9.0k points