$\"\"$

\

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

\

Find the initial quantity.

\

The general form of amount of radium isotope is $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

Apply logarithm on both sides.

\

$\"\"$

\

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

\

$\"\"$

\

Amount of isotope after $\"\"$ years is

\

General form is $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The initial quantity is $\"\"$ .

\

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

\

Amount of radium isotope is $\"\"$ .

\

$\"\"$

\

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

\

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

\

$\"\"$

\

$\"\"$ g

\

The amount after $\"\"$ years is $\"\"$ g.

\

$\"\"$

\

The initial quantity is $\"\"$ .

\

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