Final answer:
Long-term Potentiation (LTP) is the correct answer, which is a process that leads to a persistent strengthening of a postsynaptic cell's response to a stimulus, facilitating learning and memory.
Step-by-step explanation:
The enhancement of a postsynaptic cell's response to a constant stimulus over a period of time from hours to weeks is known as Long-term Potentiation (LTP). LTP is the persistent strengthening of synaptic connections based on the Hebbian principle which is often summarized as 'cells that fire together wire together.' This process involves a cascade of events starting with the depolarization of the postsynaptic neuron. Depolarization forces magnesium ions out of NMDA (N-Methyl-D-aspartate) receptors, allowing Ca2+ ions to enter. These ions then trigger further signaling that results in the insertion of additional AMPA (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) receptors into the postsynaptic membrane, enhancing the neuron's responsiveness to glutamate. This synaptic enhancement is crucial for learning and memory and is contrasted with Long-term Depression (LTD), which is a weakening of synaptic connections.