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?

Painting is 13725 years old.

Step-by-step explanation:

C-14 dating is the process through which age of fossils or dead tissues are determined.

One important thing about the C-14 dating is half life life period of C-14 that is 5730 years.

Now we know for C-14 decay we use the formula

where = present quantity of C-14

= Initial quantity of C-14

k = Decay constant

t = Duration or time

We will calculate the decay constant first to use this formula for age determination further.

For Half life of C-14

A_{t}=A_{0}e^{-kt}

Taking ln on both the sides

k =

Now we have been given in the question that C-14 found to be 19% and we have to determine the age of the painting.

We will take ln on both the sides

t = 1.3725×

t = 13725 years

Therefore, painting is 13725 years old.

13713.717 years

Step-by-step explanation:

The exponential decay model for Carbon-14 is modeled by the following formula:

where:

is the initial amount of Carbon-14

A is the final amount of Carbon-14,

t is the elapsed time in years since the painting was made

Replacing in the formula:

18

step-by-step explanation:

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