$\"\"$

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The number of bacteria in a culture is increasing according to the law of exponential growth.

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The exponential growth for bacteria population is $\"\"$ .

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Where $\"\"$ is the number of bacteria, $\"\"$ is time in hours, $\"\"$ is the initial population and $\"\"$ is the proportional constant.

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After $\"\"$ the number of bacteria is $\"\"$ .

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$\"\"$

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$\"\"$ .

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After $\"\"$ the number of bacteria is $\"\"$ .

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$\"\"$ .

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$\"\"$

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(a) Find the initial population.

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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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$\"\"$

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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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The initial population of bacteria is $\"\"$ .

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$\"\"$

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(b) Find the exponential growth model for the bacteria population.

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The exponential growth for bacteria population is $\"\"$ .

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

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$\"\"$ .

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The exponential growth for bacteria population is $\"\"$ .

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$\"\"$

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(c) Find the number of bacteria after $\"\"$ .

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The exponential growth for bacteria population is $\"\"$ .

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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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The number of bacteria after $\"\"$ is $\"\"$ .

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$\"\"$

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(d) Find the hours when bacteria count will be $\"\"$ .

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The exponential growth for bacteria population is $\"\"$ .

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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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The bacteria count will be $\"\"$ after $\"\"$ .

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$\"\"$

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(a) The initial population of bacteria is $\"\"$ .

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(b) The exponential growth for bacteria population is $\"\"$ .

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(c) The number of bacteria after $\"\"$ is $\"\"$ .

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(d) The bacteria count will be $\"\"$ after $\"\"$ .