Final answer:
Olfactory receptor neurons are replaced through neurogenesis, where new neurons are generated to replace the old ones. These new neurons extend their axons into the central nervous system by following the existing fibers of the olfactory nerve.
Step-by-step explanation:
The olfactory receptor neurons are replaced through a process called neurogenesis. The sensory neurons of the olfactory epithelium have a limited lifespan of approximately one to four months, after which new neurons are generated to replace them. These new neurons extend their axons into the central nervous system by growing along the existing fibers of the olfactory nerve.