Final answer:
Diagnosis-related groups (DRGs) are the prospective payment system that determines Medicare reimbursement for an elderly patient's hospital care.
Step-by-step explanation:
The prospective payment system responsible for determining the reimbursement for a Medicare patient's care in an acute care hospital is the Diagnosis-related groups (DRGs). Medicare Part A operates on this system and classifies patients into different groups based on their diagnoses, the procedures they undergo, age, sex, and discharge status. Hospitals are then paid a fixed rate for the entire hospital stay of a patient within each DRG. This predetermined rate is meant to cover all charges associated with an inpatient stay, from bed and board to tests, drugs, and surgeries.