$\"\"$

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(a)

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The amount $\"\"$ is the number of population of the city and $\"\"$ is the time in years,then $\"\"$ as a function of $\"\"$ is $\"\"$ .

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Where $\"\"$ is the initial population of the city and $\"\"$ is a rate of decay.

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Therefore,the function is $\"\"$ .

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$\"\"$

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(b)

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The function is $\"\"$ .

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The current population is $\"\"$ .

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If the population doubled in size over an $\"\"$ months period.

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Hence, $\"\"$

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The time period is $\"\"$ .

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Substitute all the values in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Take natural logarith on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The rate of decay is $\"\"$ per hour.

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$\"\"$

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The function is $\"\"$ .

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Find the popluation after two years.

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Hence, $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the function.

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$\"\"$

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$\"\"$

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The population of the city after two years is $\"\"$ .

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$\"\"$

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(a) The function is $\"\"$ .

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(b) The population of the city after two years is $\"\"$ .