$\"\"$

\

Newtons Law of Cooling is $\"\"$

\

Here $\"\"$ is the temperature of the object and $\"\"$ is the surrondings temperature.

\

Change in temperature $\"\"$ .

\

At the intital time $\"\"$

\

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

\

Substitute $\"\"$ and $\"\"$ in the equation $\"\"$ .

\

$\"\"$ .

\

The general exponential decay function is $\"\"$ .

\

Substitute $\"\"$ in the above equation.

\

$\"\"$

\

$\"\"$

\

After ten minutes, the temperature is stein is $\"\"$ then $\"\"$ .

\

Hence $\"\"$ .

\

substitute $\"\"$ and $\"\"$ in the above equation

\

$\"\"$ .

\

Substitute $\"\"$ in the equation $\"\"$ at $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Therefore,the decay constant is $\"\"$

\

$\"\"$

\

The equation is $\"\"$ .

\

Find the temperature after $\"\"$ minutes.

\

Hence , $\"\"$ .

\

The equation is $\"\"$ .

\

$\"\"$ .

\

Temperature after $\"\"$ minutes :

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in the equation $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

Temperature after $\"\"$ minutes is $\"\"$ .

\

$\"\"$

\

The equation is $\"\"$ .

\

Find the time to reach a temperature of $\"\"$

\

The equation is $\"\"$ .

\

Substittue $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$

\

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

\

$\"\"$

\

Stein reach a temperature of $\"\"$ in $\"\"$ minutes.

\

$\"\"$

\

Temperature after $\"\"$ minutes is $\"\"$ and Stein reach a temperature of $\"\"$ in $\"\"$ minutes.