The law is not as you state although it often gets reported as this. The 'A''$A$' you quote is the optical density. TheThe Beer-Lambert law is $I_{tr}=I_0e^{-\epsilon_\lambda [C]L}$$I_{tr}=I_0e^{-\epsilon_\lambda [C]\ell}$ where $I_{tr}$ is the intensity of transmitted light for a molecule at concentration [C]$[C]$ at wavelength $\lambda$ and cell path length L.$\ell$, and $\epsilon_\lambda$ is the extinction coefficient at wavelength $\lambda$.
From the definition you can see where the expression you ask about comes from even with their different notation; it looks as if $w=-{\epsilon_\lambda [C]L}$$w=-{\epsilon_\lambda [C]\ell}$ where ${\epsilon_\lambda [C]L}$${\epsilon_\lambda [C]\ell}$ is the optical density.