Final answer:
The synthesis and secretion of insulin start in the endoplasmic reticulum, proceed with modification in the Golgi apparatus, and finish with secretion at the cell membrane. Option b is correct.
Step-by-step explanation:
The correct sequence of the pathway for the synthesis and secretion of insulin by the β-cells of the pancreas is: Endoplasmic reticulum → Golgi apparatus → Cell membrane.
The process begins with the synthesis of preproinsulin on the ribosomes attached to the rough endoplasmic reticulum. This preproinsulin is then processed into proinsulin in the rough ER, where it folds and forms disulfide bonds.
Next, the proinsulin is transported to the Golgi apparatus in vesicles where it is further modified into mature insulin. Finally, mature insulin is packed into secretory vesicles which then travel to the cell membrane, ready to be secreted into the bloodstream in response to high blood glucose levels.
Hence, option b is correct.