$\"\"$

\

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

\

The half-life of radium is $\"\"$ years.

\

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

\

The initial amount is $\"\"$ grams.

\

Substitue all the values.

\

$\"\"$

\

$\"\"$

\

Apply natural logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

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

\

$\"\"$

\

Find the amount of radium in $\"\"$ years.

\

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

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ grams.

\

Therefore, the amount of radium is left after $\"\"$ years is $\"\"$ grams.

\

$\"\"$

\

The amount of radium is left after $\"\"$ years is $\"\"$ grams.