Final answer:
The cranial nerve associated with olfaction is Cranial Nerve I, consisting of the axons of olfactory sensory neurons that connect the nasal olfactory epithelium to the olfactory bulb and then to the brain regions involved in processing smells.
Step-by-step explanation:
The cranial nerve associated with olfaction, or the sense of smell, is Cranial Nerve I. This nerve, also known as the olfactory nerve, is made up of the axons of olfactory sensory neurons. These neurons are bipolar neurons with a single dendrite in the nasal olfactory epithelium. The axons of these neurons extend from the basal surface of the epithelium, through an olfactory foramen in the cribriform plate of the ethmoid bone, and synapse with the neurons of the olfactory bulb. From the olfactory bulb, the olfactory tract connects to the olfactory cortex in the temporal lobe, as well as to parts of the limbic system and hypothalamus.
Seeing as this system is involved in detecting and processing odors, the olfactory nerve's unique connection to the cerebral cortex, without synapsing in the thalamus, makes smell a potent trigger for memories and emotions. Moreover, olfactory neurons in the nasal epithelium are regularly replaced and must reestablish their connections to the olfactory bulb, indicating an ongoing process of neuronal renewal and plasticity within the olfactory system.