If the water saturation in a reservoir increases while the formation resistivity remains constant, what does this mathematically imply regarding the Archie cementation exponent?

To understand this relationship, we look at Archie’s Law, which states that formation resistivity—the rock's resistance to electrical current—is determined by water saturation, porosity, the resistivity of the formation water, and the cementation exponent. The cementation exponent, denoted as m, represents how the complex, winding paths within the rock pores affect electrical flow. Mathematically, the resistivity of a formation is proportional to the water ....