$\"\"$

\

The exponential growth function is $\"\"$ .

\

The half-life of carbon 14 is $\"\"$ years.

\

Hence, time period is $\"\"$ and $\"\"$

\

Substitue all the values.

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$\"\"$

\

$\"\"$

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Apply natural logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

There,the decay constant is $\"\"$ .

\

$\"\"$

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A piece of charcoal is found to contain $\"\"$ of the carbon 14.

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When did the tree die from which the charcoal came.

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$\"\"$ and $\"\"$ .

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Susbtitute all the values in $\"\"$ .

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$\"\"$

\

$\"\"$

\

Take natural logarithm on each side.

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ years.

\

Therefore, the tree die from which the charcoal came in $\"\"$ years ago.

\

$\"\"$

\

The tree die from which the charcoal came in $\"\"$ years ago.