Final answer:
The direct mathematical relationship is between the amount of oxygen we breathe in and the energy our body requires, facilitated by the process of cellular respiration and represented by the respiratory quotient.
Step-by-step explanation:
There is a direct mathematical relationship between the amount of oxygen we breathe in and the amount of energy the body requires. In the body, oxygen is used by cells to produce energy, and carbon dioxide is produced as a waste product. This relationship is quantified by the respiratory quotient (RQ), which varies depending on the type of fuel used by the body, such as glucose, protein, and fat.
The RQ is typically about 0.7 for fat and about 0.8 for protein, indicating that less carbon dioxide is produced relative to the amount of oxygen consumed. Oxygen is essential for the process of cellular respiration, where it combines with glucose to release energy, and without adequate oxygen, our cells cannot produce sufficient energy to meet the body's demands.