Chemical reactions as exponential functions

Are all graphs of molar concentration vs. time, for the reactants, exponential decay functions? (Until equilibrium is reached, if it goes to equilibrium at all.)

If so, intuitively, why is that the case?

EDIT: @ShankRam has brought it to my attention that zero-order reactions do not entail exponential decay functions. However, I would still like to know if first-order and second-order reactions do, and why they do.

Intuitively, we can understand why only a first order reaction (at least for noncomplex reaction orders) displays exponential decay because a first order reaction implies that the rate of decay ($d[A]\over dt$) is proportional to the concentration ($[A]$). This relationship precisely describes an exponential function.