$\"\"$

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The function is $\"\"$ for $\"\"$ .

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a.

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Graph the function for $\"\"$ .

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Graph the function $\"\"$ .

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$\"\"$

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$\"\"$

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b.

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Find the horizontal asympote.

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Graph the function $\"\"$ .

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$\"\"$

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Observe the graph:

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The horizontal asympote is $\"\"$ .

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$\"\"$

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c.

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Find the maximum population.

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The maximum population is approaches the asymptote.

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Maximum population will be little less than $\"\"$ .

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d.

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Find the reach of population at $\"\"$ .

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$\"\"$ (Population formula)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Cross product)

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$\"\"$ (Simplify)

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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$\"\"$ (Take ln on each side)

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$\"\"$ ( $\"\"$ )

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$\"\"$ (Substitute: $\"\"$ )

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Cancel common terms)

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The population reaches $\"\"$ after about $\"\"$ years.

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$\"\"$

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a.

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Graph the function $\"\"$ .

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$\"\"$

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b. The horizontal asympote is $\"\"$ .

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c. The maximum population will be $\"\"$ .

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d. The population reaches $\"\"$ after about $\"\"$ years.