$\"\"$

\

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

\

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

\

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

\

Substitue all the values.

\

$\"\"$

\

$\"\"$

\

Apply natural logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

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

\

$\"\"$

\

A fossilized leaf contains $\"\"$ of its normal amount of carbon 14.

\

Find the age of the fossil.

\

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

\

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

\

$\"\"$

\

$\"\"$

\

Take natural logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ years.

\

Therefore, The age of the fossil is $\"\"$ years.

\

$\"\"$

\

The age of the fossil is $\"\"$ years.