In fact answer is medulla because it is the one which have rhymth centre of body but acc. to ncert it is pons it is a chemisentive area which decreses the inspiration phase and hence the expiration phase increses so that co2 exhale more and more but it is controlled by medulla only

Respiration Control by Medulla and Pons
The central nervous system plays a crucial role in regulating respiration, primarily through two brain structures: the medulla oblongata and the pons. Both structures work together to maintain normal respiratory rhythms and respond to metabolic demands.
Medulla Oblongata
- The medulla is the primary control center for respiration.
- It contains the ventral respiratory group (VRG) and dorsal respiratory group (DRG), which are responsible for initiating and maintaining rhythmic breathing.
- The VRG is involved in both inhalation and exhalation, while the DRG processes sensory information and adjusts breathing patterns as needed.
- It responds to changes in carbon dioxide and oxygen levels, ensuring that gas exchange meets the body’s needs.
Pons
- The pons serves as a bridge between different parts of the brain and modulates the activity of the medulla.
- It houses the pneumotaxic center, which regulates the duration of inhalation, contributing to the rhythm of breathing.
- The apneustic center in the pons promotes prolonged inhalation and can influence the pattern of respiration.
- By fine-tuning signals from the medulla, the pons ensures smooth transitions between inhalation and exhalation.
Integration of Functions
- Together, the medulla and pons maintain a balance between the involuntary and voluntary control of breathing.
- They adapt respiratory patterns during activities such as exercise, speaking, or sleeping, reflecting the body’s immediate needs.
- Neurochemical signals and sensory inputs from peripheral receptors influence their activity, ensuring effective respiratory control.
In summary, both the medulla and pons are essential for the regulation of respiration, with each structure contributing uniquely to the overall respiratory rhythm and response to physiological changes.