$\"\"$

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The mass at time $\"\"$ is $\"\"$ , where is $\"\"$ the initial mass and $\"\"$ is a negative constant.

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The mean life $\"\"$ of an atom in the substance is $\"\"$ .

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The value is $\"\"$ .

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Find the mean life of a $\"\"$ atom.

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$\"\"$ .

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$\"\"$ .

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Solve the integral by using parts of integration method.

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Formula for integration by parts : $\"\"$ .

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

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Consider $\"\"$ .

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Apply integral on each side.

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$\"\"$

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$\"\"$ .

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$\"\"$

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Substitute the corresponding values in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The mean life of a $\"\"$ atom is $\"\"$ .

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$\"\"$

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The mean life of a $\"\"$ atom is $\"\"$ .