$\"\"$

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(a) Initially the number of fishes in lake are $\"\"$ .

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The carrying capacity is $\"\"$ .

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The logistic model equation is $\"\"$ , where $\"\"$ .

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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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The number of fish tripled in first year.

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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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$\"\"$

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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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The size of the population after $\"\"$ years is $\"\"$ .

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$\"\"$

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(b) How long will it take for the population to increase to $\"\"$ .

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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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$\"\"$

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$\"\"$ years.

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$\"\"$

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(a) The size of the population after $\"\"$ years is $\"\"$ .

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(b) $\"\"$ years.