$\"\"$

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(a)

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

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Find the inverse of the function.

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The function is $\"\"$ .

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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 inverse of the function is $\"\"$ .

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The inverse of the function represents the number of hours have passes when there are $\"\"$ bacteria.

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$\"\"$

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(b)

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Find the time when the population reach $\"\"$ .

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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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Therefore, the population reach $\"\"$ after $\"\"$ .

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$\"\"$

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(a) The inverse of the function is $\"\"$ .

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The inverse of the function represents the number of hours have passes when there are $\"\"$ bacteria.

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(b) The population reach $\"\"$ after $\"\"$ .