How does the structure of the membrane relate to its selective permeability? (think about the chemical properties of the inner core of the bi-layer.)

The cell membrane is also called selectively permeable membrane for the sole reason being it is selective in nature.

It forms a physical barrier and as a barrier between the cell and the external environment as it allows only selected necessary molecules to pass through it and at the same time prevents entry of unwanted / unnecessary substances.

It also regulates the entry and exit of molecules into and out of the cell.

The cell membrane permits the entry of vital molecules like

water, oxygen, amino acids and glucose into the cell as they are crucial for various life processes and at the same time metabolic waste products are expelled through the cell membrane.