Final answer:
The correct code for a returning patient with improving but persistent back pain after a recent evaluation is 99213, reflecting a low complexity medical decision making process.
Step-by-step explanation:
The code that should be used for a returning patient who comes in with back pain, which is improving but still present after being evaluated by a PCP 3 days ago, is 99213. This code is for an established patient with at least two of these three key components: an expanded problem focused history, an expanded problem focused examination, and medical decision making of low complexity. Considering the back pain is an ongoing issue and has been recently evaluated, this visit doesn't constitute a new patient visit nor does it require the comprehensive assessments indicated by the higher-level codes such as 99214 (which implies moderate complexity) or 99215 (which implies high complexity).