The function response did not provide any specific information regarding the differences between prokaryotic and eukaryotic cell membranes. Therefore, I will summarize the relevant differences based on general knowledge.

Prokaryotic and eukaryotic cells exhibit several key differences in their cell membranes:

1. Structure and Composition:

   • Prokaryotic Cell Membranes: These membranes are primarily composed of a phospholipid bilayer and a range of proteins. They lack sterols (like cholesterol in eukaryotic cells) but may contain hopanoids, which serve a similar function in stabilizing the membrane.
   • Eukaryotic Cell Membranes: These membranes are more complex and consist of a phospholipid bilayer containing sterols, primarily cholesterol, which helps maintain membrane fluidity and integrity.

2. Function and Permeability:

   • Prokaryotic Membranes: The permeability of these membranes is often determined by the presence of specific proteins that act as channels or carriers for molecules. They may also have a rigid cell wall that provides additional structure.
   • Eukaryotic Membranes: In eukaryotes, membranes are often compartmentalized into organelles, each with distinct functions and permeabilities. Their fluid nature allows for facilitated transport and membrane fusion processes.

3. Presence of Membrane-bound Organelles:

   • Prokaryotic Cells: Generally lack membrane-bound organelles. Their functions are carried out in the cytoplasm or directly across the cell membrane.
   • Eukaryotic Cells: Contain multiple membrane-bound organelles (such as the nucleus, mitochondria, endoplasmic reticulum, etc.) which compartmentalize various biochemical processes.

4. Cell Wall Association:

   • Prokaryotes: Many prokaryotes have a cell wall that is significant for maintaining shape and protection. The membrane is located just beneath this wall.
   • Eukaryotes: While plant cells have cell walls, animal cells do not possess a cell wall, and their membranes function with more flexibility.

In conclusion, the differences between prokaryotic and eukaryotic cell membranes are critical to their overall functionality, stability, and cellular processes. Prokaryotic membranes tend to be simpler and more rigid, while eukaryotic membranes are complex and dynamic, allowing for a greater range of cellular activities.