$\"\"$

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The rate of change in sales $\"\"$ is inversely proportional to time $\"\"$ $\"\"$ , where $\"\"$ is measured in weeks.

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$\"\"$

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$\"\"$ , where $\"\"$ is proportional constant.

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Sales after $\"\"$ weeks is $\"\"$ units.

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Sales after $\"\"$ weeks is $\"\"$ units.

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Find the function $\"\"$ .

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$\"\"$

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$\"\"$

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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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$\"\"$

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in the above equation.

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$ .

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$\"\"$

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The function is $\"\"$ .