$\"\"$

\

The equation for cooling is $\"\"$ .

\

The freezer kept at constant temperature $\"\"$ .

\

The initial temperature of the liquid is $\"\"$ .

\

Find the value of $\"\"$ .

\

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

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$ .

\

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

\

$\"\"$ .

\

$\"\"$

\

After five minutes the liquid tempreture is $\"\"$ .

\

Substiute $\"\"$ and in $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Apply natural logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

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

\

$\"\"$ .

\

$\"\"$

\

Find the time taken to decrease the tempreture to $\"\"$ .

\

Substiute $\"\"$ in $\"\"$ .

\

$\"\"$

\

Already five minutes have passed, so the the time taken to decrease the tempreture to $\"\"$ is \ \ $\"\"$ .

\

$\"\"$

\

Time taken to decrease the tempreture to $\"\"$ is $\"\"$ .