Final answer:
In the context of a heavy smoker with more than 20 years of history, a BAL cell count with differential would likely show Neutrophilia, indicating an increased count of neutrophils due to chronic inflammation in the respiratory tract.
Step-by-step explanation:
The question asks about the changes in a bronchoalveolar lavage (BAL) cell count with differential in a patient with a long history of heavy smoking. The correct answer would be Neutrophilia, which means an increase in neutrophils. Neutrophils are typically the first responders during injury or infection. A heavy smoker is likely to have chronic inflammation in the respiratory tract, which leads to the recruitment of neutrophils as part of the body's defense mechanism. Eosinophils, mentioned in the question, are primarily associated with allergic responses and parasitic infections but not typically with the effects of smoking. Lymphocytosis, an increase in lymphocytes, and monocytosis, an increase in monocytes, are usually associated with viral or fungal infections, tuberculosis, some chronic diseases, and specific leukemias, rather than with long-term smoking.