$\"\"$

\

The rate of depreciation of a machine is $\"\"$ .

\

The rate of depreciation of a machine is inversely proportional to $\"\"$ :

\

$\"\"$

\

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

\

Where $\"\"$ is the value of machine $\"\"$ years after it was purchased.

\

$\"\"$

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

Find the value of $\"\"$ .

\

The initial value of the machine is $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

$\"\"$

\

The value of the machine decreased in the first year is $\"\"$ .

\

$\"\"$ .

\

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

\

$\"\"$

\

$\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Estimate the value of machine after four years.

\

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

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

The value of machine after four years is $\"\"$ .

\

$\"\"$

\

The value of machine after four years is $\"\"$ .