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If an initial quantity $\"\"$ continuous grows at an exponential rate $\"\"$ , then the final amount $\"\"$ after a time $\"\"$ is given by the following formula $\"\"$ . $\"\"$

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A certain bacterium used to treat oil spills has a doubling time of $\"\"$ minutes.

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A colony begins with a population of one bacterium $\"\"$ .

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Since bacterium used to treat oil spills has a doubling $\"\"$ .

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Substitute $\"\"$ in $\"\"$ we get $\"\"$ .

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

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$\"\"$

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Apply logarithm on each side.

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a)

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Find modeling equation for exponential growth.

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

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$\"\"$ .

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Modeling equation for exponential growth $\"\"$ .

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$\"\"$

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(b)

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Find how many bacteria will be present after $\"\"$ minutes.

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

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$\"\"$

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$\"\"$ .

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Number of bacteria will be present after $\"\"$ minutes is $\"\"$ .

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$\"\"$

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(c)

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Find how long it will take for the colony to grow $\"\"$ bacteria.

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Since a population of $\"\"$ bacteria is sufficient to clean a small oil spill $\"\"$ .

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substitute $\"\"$ , $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Apply logarithm on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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Time taken for the colony to grow $\"\"$ bacteria is $\"\"$ minutes.

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$\"\"$

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(a) Modeling equation for exponential growth $\"\"$ .

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(b) Number of bacteria will be present after $\"\"$ minutes is $\"\"$ .

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(c) Time taken for the colony to grow $\"\"$ bacteria is $\"\"$ minutes.