Final answer:
The nurse should obtain blood glucose levels as the next assessment data. The increased respiratory rate and depth, along with the patient becoming lethargic, suggest ketoacidosis as a complication of type 1 diabetes mellitus. Ketoacidosis occurs due to a lack of insulin, causing the body to break down fat for energy, resulting in the production of ketones.
Step-by-step explanation:
The nurse should obtain blood glucose levels as the next assessment data. The increased respiratory rate and depth, along with the patient becoming lethargic, are indicative of ketoacidosis, a serious complication of type 1 diabetes mellitus. Ketoacidosis occurs when there is a lack of insulin, causing the body to break down fat for energy, resulting in the production of ketones. High levels of ketones can lead to the characteristic deep and rapid breathing seen in the patient.