$\"\"$

\

The exponential function is $\"\"$ .

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

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

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

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$\"\"$

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$\"\"$

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Apply logarithm on each side.

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$\"\"$

\

$\"\"$

\

$\"\"$

\

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

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$\"\"$

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

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The equation is $\"\"$ .

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The initial quantity is $\"\"$ .

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ grams.

\

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

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. $\"\"$

\

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

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The equation is $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ grams.

\

Therefore, the amount after $\"\"$ years is $\"\"$ .

\

$\"\"$

\

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

\

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