Explanation
According to the BABOK® Guide, a change-driven approach of business analysis is one that "emphasizes rapid delivery of business value in short iterations" (p. 31). This approach allows for frequent feedback and validation of the requirements and the solution, as well as adaptation to changing business needs and priorities.
The project manager's authority to approve the requirements based on the short iterations of business analysis activities indicates that this approach is being used in this scenario. The other options are not correct because:
Progressive elaboration is a technique of gradually refining the level of detail and accuracy of the requirements as more information becomes available, not an approach of business analysis (p. 36).
Plan-driven approach is one that "emphasizes upfront definition of the requirements and the plan to deliver the solution" (p. 31). This approach requires more formal approval and change control processes than the change-driven approach.
Iterative approach is a generic term that can apply to both plan-driven and change-driven approaches, as long as they involve repeating cycles of analysis and delivery (p. 31). It is not a specific approach of business analysis by itself. References:
BABOK® Guide, p. 31, 36
Business Analysis: Definition, Process, Techniques and Tips, section "What are the different types of business analysis techniques?"