For this problem T is the variable for the temperature, k is the growth constant (or constant of proportionality) and is positive.
Newton's Law of cooling states that the temperature of an object changes at a rate proportional to the difference of the temperature of the surrounding medium and the temperature of the object. If the temperature of the surrounding medium is $240^\circ F$ write a differential equation to model the situation.
Differential equation: $= 0$
This is a separable differential equation:
$T^\prime = k$
Integrating both sides with respect to t (using C as the constant of integration) we get
=
The temperature of the object is given by $T =$