The equation provided is:
\(^{146}\text{C} \rightarrow {}^{147}\text{N} + 0^{-1}e\)
This model represents the transformation of Carbon-146 (C) into Nitrogen-147 (N) while emitting a beta particle (denoted as \(0^{-1}e\)).
Since the emission of a beta particle indicates that a neutron is converted into a proton, this process is classified as beta-minus decay.
Therefore, the correct response is:
beta-minus decay