Newton's law of cooling says that the rate of cooling of an object is proportional to the difference between the temperature of the object and that of its surroundings (provided the difference is not too large). If $T = T(t)$ represents the temperature of a (warm) object at time $t$, $A$ represents the ambient (cool) temperature, and $k$ is a negative constant of proportionality, which equation(s) accurately characterize Newton's law?

A. $\frac{dT}{dt} = kT (T - A)$
B. $\frac{dT}{dt} = kT (1 - T/A)$
C. $\frac{dT}{dt} = k (A - T)$
D. $\frac{dT}{dt} = k (T - A)$
E. All of the above
F. None of the above