$\"\"$

\

The exponential function is $\"\"$ .

\

Half life of the isotope is $\"\"$ .

\

At half life time, $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Apply logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

Therefore, the exponential equation is $\"\"$ .

\

$\"\"$

\

The amount of isotope after $\"\"$ years is $\"\"$ .

\

Find $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in the exponential equation.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Initial quantity is $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

Find the amount of isotope after $\"\"$ years.

\

Substitute $\"\"$ in the exponential equation.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The amount of isotope after $\"\"$ years is $\"\"$ .

\

$\"\"$

\

Initial quantity is $\"\"$ .

\

The amount of isotope after $\"\"$ years is $\"\"$ .