Final answer:
When a patient is hemorrhaging and in shock due to a gunshot wound, their heart rate will likely be increased as a response to circulatory shock, as the body tries to maintain blood pressure and perfusion.
Step-by-step explanation:
If a patient enters the Emergency Room (ER) with a gunshot wound to the leg and is hemorrhaging and in shock, their heart rate will most likely be increased. This increase in heart rate is a physiological response to circulatory shock, where the loss of blood leads to the circulatory system's inability to maintain adequate blood flow to supply oxygen and nutrients to the tissues. In shock, the body attempts to compensate for the low blood volume by increasing the heart rate in an effort to maintain blood pressure and perfusion to vital organs.