Final answer:
Decreasing sodium permeability from rest results in hyperpolarization of the membrane potential, making the interior of the cell more negative and increasing the difficulty for neurons to fire an action potential.
Step-by-step explanation:
Decreasing sodium permeability from rest would lead to a hyperpolarization of the membrane potential. At the resting potential, the inside of the cell is more negative relative to the outside, with a value typically around -70 millivolts (mV). When the membrane permeability for sodium decreases, less sodium enters the cell, which means there is less depolarization occurring, causing the cell interior to become more negatively charged compared to the exterior. This would drive the membrane potential further away from zero, creating a hyperpolarization state. Hyperpolarization can increase the difficulty for a neuron to reach the threshold needed to fire an action potential.