$\"\"$

\

The exponential function is $\"\"$ .

\

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

\

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

\

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

\

$\"\"$

\

$\"\"$

\

Apply logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

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

\

Find remaining percentage of amount after $\"\"$ years .

\

The equation is $\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Therefore, $\"\"$ remains after $\"\"$ years.

\

$\"\"$

\

$\"\"$ amount remains after $\"\"$ years.