How do endocytosis and exocytosis maintain homeostasis within the cell?
Endocytosis allows large molecules to enter the cell, and exocytosis expels large molecules from the cell. In this way, the cell can obtain things it needs and get rid of things it doesn't.
In endocytosis, the cell membrane bends in and surrounds some particles (usually carbohydrates or proteins). The membrane pinches in a creates a vesicle, like a storage compartment. See the image below:
This could allow the cell to take in food particles or maybe for a white blood cell to engulf a foreign bacterial cell.
Exocytosis is the reverse process, where a cell expels large particles, usually waste from cellular processes.
These processes both require energy but are important for the cell to maintain homeostasis (which is the maintenance of an internal stable environment). They allow the cell to take in and get rid of large particles.