$\"\"$

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The logistic model equation is $\"\"$ , where $\"\"$ is the time in days.

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Find the average population over the interval $\"\"$ .

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Average value of the function $\"\"$ on $\"\"$ is defined as $\"\"$ .

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In this case $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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

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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 $\"\"$ .

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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 average population is $\"\"$ .

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$\"\"$

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The average population is $\"\"$ .