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

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Half life of carbon - $\"\"$ is $\"\"$ thousand years.

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since Half life of carbon - $\"\"$ is $\"\"$ .

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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 decay.

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

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$\"\"$

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Modeling equation for exponential decay is $\"\"$ .

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$\"\"$

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(b)

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Find how many grams of carbon- $\"\"$ will remain after $\"\"$ thousand years.

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Initial carbon- $\"\"$ is $\"\"$ grams.

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

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$\"\"$

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$\"\"$ grams.

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carbon- $\"\"$ will remain after $\"\"$ thousand years is $\"\"$ grams.

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$\"\"$

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(c)

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Find when only $\"\"$ gram of the original $\"\"$ grams of carbon- $\"\"$ will remain.

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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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$\"\"$ gram of the original $\"\"$ grams of carbon- $\"\"$ will remain in $\"\"$ thousand years.

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$\"\"$

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(a) Modeling equation for exponential decay is $\"\"$ .

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(b)

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carbon- $\"\"$ will remain after $\"\"$ thousand years is $\"\"$ grams.

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(c)

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$\"\"$ gram of the original $\"\"$ grams of carbon- $\"\"$ will remain in $\"\"$ thousand years.