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If an initial quantity $\"\"$ grove or decays at an exponential rate $\"\"$ , then the final amount $\"\"$ after a time $\"\"$ is given by the following formula $\"\"$ $\"\"$

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(a)

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Find how many articles made up the encyclopedia in $\"\"$ .

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The number of articles, $\"\"$ , t years after $\"\"$ can be modeled by $\"\"$ .

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At $\"\"$ the time period is $\"\"$ .

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

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$\"\"$

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Number of article made up the encyclopedia in $\"\"$ is $\"\"$ .

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Find the rate number of articles increased.

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Compare exponential modeling function $\"\"$ with $\"\"$ .

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$\"\"$

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$\"\"$ .

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Rate of number of articles increased is $\"\"$ . $\"\"$

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(b)

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Find during which year did encyclopedia reach $\"\"$ million articles.

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Since encyclopedia reach $\"\"$ million articles $\"\"$ .

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Substitute $\"\"$ 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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Encyclopedia reach $\"\"$ million articles after $\"\"$ years i.e $\"\"$ .

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$\"\"$

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(c)

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Find number of articles there will be at the beginning of $\"\"$ .

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Time period between $\"\"$ to $\"\"$ is $\"\"$ years.

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

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$\"\"$

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$\"\"$

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Number of articles there will be at the beginning of $\"\"$ is $\"\"$ .

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$\"\"$

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(a)

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Number of article made up the encyclopedia in $\"\"$ is $\"\"$ .

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Rate of number of articles increased is $\"\"$ .

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(b)

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Encyclopedia reach $\"\"$ million articles after $\"\"$ years i.e $\"\"$ .

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(c)

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Number of articles there will be at the beginning of $\"\"$ is $\"\"$ .