In accordance with the PMBOK® Guide, the Control Costs process is the function of monitoring the status of the project to update the project costs and managing changes to the cost baseline.

Why Control Costs (Choice D) is correct: This process involves ensuring that all change requests are acted upon in a timely manner and managing the actual changes when they occur. When a budget change is approved (even by the Project Manager within their delegated authority or through the formal Perform Integrated Change Control process), the actual implementation and monitoring of that budget adjustment fall under Control Costs. This process ensures that the cost baseline is updated to reflect the approved changes.

Estimate Costs (Choice B): This is the process of developing an approximation of the monetary resources needed to complete project work. It occurs during the planning phase, not during the execution or monitoring phase when a change to an established budget would occur.

Determine Budget (Choice C): This process involves aggregating the estimated costs of individual activities or work packages to establish an authorized cost baseline. While this establishes the budget, the act of making a change to it during the project ' s execution is a " control " function.

Manage Cost Plan (Choice A): This is not a formal PMI process. The relevant planning process is Plan Cost Management, which establishes the policies and procedures for planning, managing, expending, and controlling project costs.

The Control Costs process specifically includes " influencing the factors that create changes to the authorized cost baseline " and " managing the actual changes when and as they occur, " making it the correct engaged process for this scenario.