Final answer:
The dorsal respiratory group (DRG) is active during quiet breathing, facilitating inspiration, while the ventral respiratory group (VRG) is active during forced breathing associated with activities like exercise.
Step-by-step explanation:
The dorsal respiratory group (DRG) is active during quiet breathing, which occurs at rest. It maintains a constant breathing rhythm by stimulating the diaphragm and intercostal muscles to contract for inspiration. Conversely, when the DRG ceases activity, it results in expiration as these muscles relax. On the other hand, the ventral respiratory group (VRG) is active during forced breathing such as that which occurs during exercise or when active thought requires muscle contraction. The VRG stimulates the contraction of accessory muscles involved in respiration to induce both forced inspiration and forced expiration.