# Can Newton's Law of Cooling be used to describe heating?

Yes. If $A$ is the ambient temperature of the room and ${T}_{0}$ is the initial temperature of the object in the room, Newton's Law of Cooling/Heating predicts the temperature $T$ of the object will be given as a function of time by $T = A + \left({T}_{0} - A\right) {e}^{- k t}$, where $- k < 0$. If ${T}_{0} > A$, this model predicts cooling (a decreasing function) and if ${T}_{0} < A$, this model predicts heating (an increasing function).
In terms of calculus-related ideas, this equation can be rewritten as $T - A = \left({T}_{0} - A\right) {e}^{- k t}$ and can be interpreted as saying that the function $T - A$ undergoes exponential decay (a constant relative rate of decay) to zero as time $t$ increases (from above if ${T}_{0} > A$ and from below if ${T}_{0} < A$).