Final answer:
Atrial fibrillation is likely the cause of the irregular heart rate and pulse deficit. The Purkinje fibers have the slowest inherent rate of firing in the heart conduction system, at 15-20 impulses per minute.
Step-by-step explanation:
The irregular heart rate of around 100 beats per minute combined with a significant pulse deficit in an 83-year-old resident at a long-term care facility could be indicative of an arrhythmia. The history component that would likely produce such symptoms is d) Atrial fibrillation. Atrial fibrillation is characterized by an abnormal electrical pattern before the QRS complex and an increased frequency between QRS complexes, which can lead to an irregular heartbeat as well as a pulse deficit when not all heartbeats result in adequate blood ejection, hence not all heartbeats produce a pulse that can be detected peripherally.
Regarding your secondary question: Which component of the heart conduction system would have the slowest rate of firing?, the correct answer is d) Purkinje fibers. The inherent rate of firing for Purkinje fibers is 15-20 impulses per minute, which is slower than the atrioventricular node, atrioventricular bundle, and bundle branches.