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Tachypnea refers to an increased respiratory rate, a phenomenon that can occur under various circumstances, particularly when an animal engages in vigorous activity. During increased exercise, the demand for oxygen rises significantly, leading animals to breathe faster to meet their body's needs. This respiratory response ensures that oxygen is delivered efficiently to the muscles and that carbon dioxide, a byproduct of metabolism, is expelled adequately.

In contrast, calm resting and deep sleep typically involve a slower, more regular breathing pattern since the metabolic demands of the body are lower during these states. Similarly, after eating, animals may experience a temporary increase in their heart rate due to the digestive process, but this does not consistently lead to tachypnea as the body's demand for oxygen does not significantly spike in a way that necessitates faster breathing. Thus, increased exercise stands out as a situation where tachypnea is most likely to be observed in animals.