Final answer:
Archie is likely to use exposition as the rhetorical mode for his essay since he plans to compare and contrast a topic or redefine a term, which aligns with the explanatory and clarificatory nature of expository essays. So the correct answer is Option A.
Step-by-step explanation:
Based on the descriptions provided, Archie is MOST likely going to be writing in the mode of exposition. If he is comparing and contrasting a topic, or re-defining a term, both scenarios involve explaining or clarifying a topic or concept. An expository essay is one that explains or clarifies a topic to the reader, breaking down the topic into parts and explaining each component. This mode fits the scenario more than persuasive, narrative, or descriptive modes, as the primary purpose here is to inform and explain, as opposed to arguing for or against a specific viewpoint (persuasive), telling a story (narrative), or providing detailed sensory impressions of a subject (descriptive).
Archie's essay, therefore, would likely use comparison and contrast or definition as reasoning strategies, both of which are examples of reasoning strategies often used in expository essays. The use of these strategies will help Archie to fulfill his goal of investigating an idea and expressing a clear explanation or redefinition.