Why does breathing rate increase during and just after exercise?

During exercise your muscles work harder and need much more energy, so they respire faster and need more oxygen while producing more carbon dioxide. The rise in carbon dioxide in the blood is detected by the brain, which signals the breathing muscles to work faster and deeper to take in more oxygen and remove carbon dioxide quickly. Breathing stays fast even after you stop because during intense exercise your muscles partly used anaerobic respiration, producing lactic acid. To break down this lactic acid your body needs extra oxygen, called the oxygen debt or excess post-exercise oxygen consumption. So you keep breathing hard until enough oxygen is supplied to clear the lactic acid and restore your muscles to their normal resting state.