Which of the following diabetic medications has the lowest risk of hypoglycemia with exercise?

Metformin is the correct choice as it has the lowest risk of hypoglycemia, especially during exercise. It works primarily by reducing hepatic glucose production and improving insulin sensitivity, which generally does not lead to significant insulin secretion. This characteristic minimizes the risk of blood glucose levels dropping dangerously low, particularly when engaging in physical activity.

In contrast, other options such as glipizide, repaglinide, and glimepiride increase insulin secretion from the pancreas. These medications can increase the risk of hypoglycemia since they promote higher levels of insulin, which can lead to lower blood sugar levels if not properly managed, especially during periods of increased physical exertion when glucose utilization by the muscles increases. The potential for hypoglycemia is a critical consideration in geriatric patients, as they may have various risk factors or comorbidities that exacerbate this risk. Therefore, metformin's mechanism and profile make it a safer choice in this context.