The advent of Large Language Models (LLMs) and generative AI is fundamentally transforming information retrieval and processing on the Internet, bringing both great potential and significant concerns regarding content authenticity and reliability. This paper presents a novel quantitative approach to shed light on the complex information dynamics arising from the growing use of generative AI tools. Despite their significant impact on the digital ecosystem, these dynamics remain largely uncharted and poorly understood. We propose a stochastic model to characterize the generation, indexing, and dissemination of information in response to new topics. This scenario particularly challenges current LLMs, which often rely on real-time Retrieval-Augmented Generation (RAG) techniques to overcome their static knowledge limitations. Our findings suggest that the rapid pace of generative AI adoption, combined with increasing user reliance, can outpace human verification, escalating the risk of inaccurate information proliferation across digital resources. An in-depth analysis of Stack Exchange data confirms that high-quality answers inevitably require substantial time and human effort to emerge. This underscores the considerable risks associated with generating persuasive text in response to new questions and highlights the critical need for responsible development and deployment of future generative AI tools.