Final answer:
A rapid and shallow breathing pattern with a rate of 40 can be life-threatening due to the risk of excessive ventilation. Immediate medical attention is required.
Step-by-step explanation:
If a woman of advanced age has fallen and injured her ribs, and you find that she is breathing rapidly and shallowly with a rate of 40, this emergency can be life-threatening because of the risk of excessive volume of air per minute. When the respiratory rate is high and the volume per breath is low, the total volume of air inhaled per minute can be excessive, which can lead to hyperventilation and respiratory failure. This rapid and shallow breathing pattern is often a sign of a serious respiratory problem and requires immediate medical attention.