$\"\"$

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Isotope $\"\"$ is half life in year $\"\"$ .

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Find the initial quantity :

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Half life to find $\"\"$ .

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The general form of carbon isotope initial quantity is $\"\"$ , where, $\"\"$ is $\"\"$ and $\"\"$ is $\"\"$ .

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$\"\"$ .

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$\"\"$

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Apply ln on both sides.

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$\"\"$

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$\"\"$

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Substitute plug for $\"\"$ for $\"\"$ and $\"\"$ for $\"\"$ and $\"\"$ in the general form.

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$\"\"$

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To find the Amount after $\"\"$ years:

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General form is $\"\"$

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Substitute $\"\"$ and $\"\"$ in the $\"\"$

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$\"\"$

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

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$\"\"$

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The initial quantity is $\"\"$ .

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