$\"\"$

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The initial amount is $\"\"$ million dollars.

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The rate of disbursement is $\"\"$ .

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The rate of disbursement is proportional to $\"\"$ :

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$\"\"$

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$\"\"$ , where $\"\"$ is proportional constant.

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The amount that remains to be disbursed is $\"\"$ .

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The time $\"\"$ is measured in days.

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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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Let $\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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

\

$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

\

$\"\"$ .

\

$\"\"$

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Find the value of $\"\"$ .

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All the money will be disbursed in $\"\"$ days.

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$\"\"$ .

\

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

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$\"\"$ .

\

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

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$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$ .

\

Find the amount that remains to be disbursed in $\"\"$ days.

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

The amount that remains to be disbursed in $\"\"$ days is $\"\"$ .

\

$\"\"$

\

The amount that remains to be disbursed in $\"\"$ days is $\"\"$ .