A fossil is discovered that has only 12.5% of the carbon-14 that it would have had originally (when the animal was alive). If the half-life of carbon-14 is 5700 years, approximately how old is the fossil?

The fossil is 17,100 years old.

Explanation:

The decay equation:

Integrating both sides

When t=0, N= = initial amount

The decay equation is

Given that,

The half life of carbon - 14 is 5700 years.

For half life,

To find the value of  , we need to put the value of N and t in the decay equation.

            [ Divided both sides]

Taking ln both sides

            [ ]

                     [ln 1= 0]

The fossil has only 12.5% of the carbon carbon-14 that it would have had originally.

So,

Then,

Taking ln both sides

The fossil is 17,100 years old.

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