Because the brain stem is what transfers all information to the rest of your body. Also, it is directly connected to the hypothalamus, which if damaged, can take away your ability to breathe or do simple tasks.
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Answer:
When you are exercising, your muscles need extra oxygen some three times as much as resting muscles.
This need means that your heart starts pumping faster, which makes for a quicker pulse. Meanwhile, your lungs are also taking in more air, hence the harder breathing