Mount Sinai opened its geriatric emergency department, or geri-ed, two months ago, modeling it in part after one at St. Joseph’s Regional Medical Center in Paterson, N.J., which opened in 2009. Hospitals also have strong financial incentives to focus on the elderly. People over 65 account for 15 percent to 20 percent of emergency room visits, hospital officials say, and that number is expected to grow as the population ages. Under the Affordable Care Act, hospitals' Medicare payments will be tied to scores on patient satisfaction surveys and how frequently patients have to be readmitted to the hospital.