$\"\"$

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Exponential growth and Decay model :

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If $\"\"$ is a differentiable function of $\"\"$ such that $\"\"$ and $\"\"$ for some constant $\"\"$ ,

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then $\"\"$ .

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$\"\"$ is the initial value of $\"\"$ and $\"\"$ is the proportional constant.

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Exponential growth occurs when $\"\"$ , and exponential decay occurs when $\"\"$ .

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$\"\"$

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Find value of $\"\"$ .

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At the initial time there are $\"\"$ and after one hour there are $\"\"$ .

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Hence, $\"\"$ and $\"\"$ .

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Susbstitute $\"\"$ and $\"\"$ 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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Therefore, the proportional constant is $\"\"$ .

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$\"\"$

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Find the time to change $\"\"$ of the compound.

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The remaining compound is

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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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$\"\"$ hours.

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$\"\"$

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$\"\"$ hours.