When observing faint objects, what is the non-linear relationship for M33 visibility between an average observer in suburban skies versus dark skies?

It may be visible with a 4-inch refractor in dark skies, but realistically requires 10 inches or more in suburban skies.

The required light threshold for visual detection of faint targets scales severely based on both the inherent faintness of the object and the darkness of the observing environment. The text illustrates this vividly with the Triangulum Galaxy (M33). In truly dark skies, an experienced observer might manage to distinguish its faint halo using a modest 4-inch aperture telescope. In contrast, for the average observer dealing with the elevated sky background typical of suburban areas impacted by light pollution, the required aperture increases significantly, becoming realistically achievable only through a 10-inch or larger instrument. This demonstrates a non-linear scaling where overcoming background sky noise demands substantially larger light-gathering capabilities.