$\"\"$ \ \

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The rate of change of $\"\"$ is proportional to $\"\"$ .

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When $\"\"$ , $\"\"$ .

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When $\"\"$ , $\"\"$ .

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The function is $\"\"$ .

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$\"\"$

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Apply integral on each side.

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$\"\"$

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$\"\"$

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Apply exponent on each side.

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$\"\"$

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$\"\"$

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$\"\"$ .

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When $\"\"$ , $\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

\

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

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$\"\"$ .

\

$\"\"$

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When $\"\"$ , $\"\"$ .

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

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

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

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$\"\"$ .

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$\"\"$

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Find the value of $\"\"$ when $\"\"$ .

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

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$\"\"$

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$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

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$\"\"$ . \ \