Final answer:
The statement that hyperpolarization occurs because the voltage-gated K+ channels close slowly is true. The delay in closing of these channels leads to excessive efflux of K+, causing hyperpolarization, an overshoot beyond the resting membrane potential.
Step-by-step explanation:
The statement that hyperpolarization occurs because the voltage-gated K+ channels close slowly is true. As an action potential is propagated down an axon, depolarization occurs first when Na+ channels open, allowing Na+ ions to enter the cell and the membrane potential to increase. Following this, repolarization occurs when the voltage-gated K+ channels open, allowing K+ ions to exit the cell.
These K+ channels open more slowly than Na+ channels and close slowly when the membrane potential repolarizes, reaching -50 mV. Due to this slow closure, K+ ions continue to leave the cell for a short period, thereby overshooting the resting membrane potential and causing the membrane to become more negative than resting potential, resulting in hyperpolarization. This overshoot is a safety mechanism that prevents the axon from being immediately excitable again, and ensures that action potentials only travel in one direction.