We can write this more mathematically using a differential equation — an equation for the unknown function $T(t)$ that also involves its derivative $\diff{T}{t}(t)\text{.}$ If we denote by $T(t)$ the temperature of the object at time $t$ and by $A$ the temperature of its surroundings, Newton's law of cooling says that there is some constant of proportionality, $K\text{,}$ such that