Final answer:
The most appropriate initial diagnostic study for a patient with signs of acromegaly is to measure growth hormone levels, which would likely be followed by a glucose tolerance test and possibly a CT scan of the brain.
Step-by-step explanation:
The most appropriate diagnostic study at this time for a 45-year-old man with symptoms suggesting acromegaly, which include an enlarged jaw, increased spaces between teeth, enlarged hands and feet, and carpal tunnel syndrome, is to measure his growth hormone levels. This condition is often caused by a growth hormone-secreting pituitary adenoma. Elevated growth hormone levels can then be confirmed with a glucose tolerance test to see if they remain high even after glucose intake, which normally suppresses growth hormone. Depending on the results, additional tests like IGF-1 levels or a CT scan of the brain might be performed to locate the adenoma.