Which of the following findings would indicate a patient is experiencing respiratory failure?

The indication that a patient is experiencing respiratory failure is often associated with signs of inadequate oxygenation or ventilation. In this context, low oxygen saturation combined with rapid breathing suggests that the patient's respiratory system is not effectively exchanging gases, which can lead to respiratory failure.

An oxygen saturation level that is lower than normal (generally below 90%) indicates that the body isn't receiving enough oxygen, and rapid breathing could be the body's attempt to compensate for this deficiency. This combination typically reflects a significant problem with the respiratory function, as the patient is either unable to get sufficient oxygen into the bloodstream or is struggling to remove carbon dioxide effectively.

By contrast, normal respiratory rates and stable vital signs, or a productive cough without respiratory distress, do not typically indicate respiratory failure, as they suggest that the respiratory and cardiovascular systems are functioning adequately. The presence of respiratory issues would also include symptoms like difficulty breathing, which is not present in the case of stable vital signs. Thus, the finding of low oxygen saturation with rapid breathing is a clear signal of respiratory compromise, aligning it firmly with the definition of respiratory failure.