$\"\"$

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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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$\"\"$

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$\"\"$

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Apply logarithm on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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

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$\"\"$

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The piece of anceint charcoal contains $\"\"$ as much of the radioactive carbon as a piece of modern char coal.

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$\"\"$

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$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .