Final answer:
The correct initial amount of air to inject into the tracheostomy tube cuff is enough to achieve a cuff pressure of 25-35 cmH2O, known as the minimal occluding volume.
Step-by-step explanation:
The respiratory therapist should initially inject air into the tracheostomy tube cuff until a pressure of 25-35 cmH2O is achieved. This is known as the minimal occluding volume, which is the least amount of air needed to achieve an airtight seal between the tube cuff and the trachea without overinflating the cuff. Overinflation can cause tracheal damage, while underinflation can lead to air leaks and aspiration of secretions. It is not advisable to inject a minimum volume of air, like 20 mL, or to inflate until firm tension is felt in the pilot balloon without measuring the cuff pressure, as this could result in incorrect cuff pressure.