$\"\"$

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(a)

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The function is $\"\"$ .

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Find number of insects at $\"\"$ days.

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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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Number of insects at $\"\"$ days is $\"\"$ .

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$\"\"$

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(b)

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The size of poulation after $\"\"$ hours is $\"\"$ .

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Where $\"\"$ is the exponential growth rate.

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The equation is $\"\"$ .

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Compare the equation with $\"\"$ .

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$\"\"$ .

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Therefore, the growth rate is $\"\"$ per day.

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$\"\"$

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(c)

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Find the population after $\"\"$ days.

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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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Number of insects after $\"\"$ days is $\"\"$ insects.

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$\"\"$

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(d)

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Find the number of days taken to reach the population of $\"\"$ insects.

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

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$\"\"$

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$\"\"$

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$\"\"$

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Take natural logarithm on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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The population of insects is $\"\"$ insects after $\"\"$ days.

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$\"\"$

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(e)

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The equation is $\"\"$ .

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Find the time when the population of the insects is double.

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Therefore, $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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Take natural logarithm on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The population of insects is double insects after $\"\"$ days.

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$\"\"$

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(a) Number of insects at $\"\"$ days is $\"\"$ insects.

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(b) The growth rate is $\"\"$ per day.

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(c) Number of insects after $\"\"$ days is $\"\"$ insects.

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(d) The population of insects is $\"\"$ insects after $\"\"$ days.

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(e) The population of insects is double insects after $\"\"$ days.