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The recent interest in precursors has been fuelled by the possibility of using them for the efficient transmission of information through absorbing media at radio or optical frequencies. Here we demonstrate that the low attenuation experienced by the Brillouin precursor is attributed to the inherently low absorption of dispersive media near DC, a characteristic already exploited with communications systems using the extremely low frequency (ELF) band. Pulses, regardless of their temporal width and carrier frequency, always obey Beer's law as long as they propagate in the linear time invariant regime. We conclude with an FDTD simulation of the Maxwell-Bloch equations that shows how optical coherent bleaching effects, which take place in the linear time variant regime of the Lorentz oscillator model, can cause sustained deviations from Beer's law over relatively long distances of water. [ABSTRACT FROM AUTHOR]