Final answer:
The central route to persuasion is the one that focuses on logic and relevant material, using data and facts in a logic-driven approach to influence an analytical and motivated audience.
Step-by-step explanation:
The processing route that focuses on logic and relevant material is the central route to persuasion. This route is characterized by a logic-driven approach that utilizes data and facts to convince individuals of an argument's worthiness. It relies on thoughtful and analytical consideration of the information presented, requiring the audience to be motivated and analytical in their processing. For example, when advertisers promote a product like a computer, they will likely use the central route to highlight the product's quality, processing speed, and memory capacity to appeal to small business owners who will value and understand these facts.