This study contributes to the emerging research on generative AI and writing pedagogy by exploring how college writing students make use of GAI when offered instruction in a range of responsible uses and latitude to integrate it into their writing process as they see fit. We analyzed chat log data and papers from participants recruited from six sections in which students were guided in experimenting with ChatGPT Plus and permitted to use it to produce up to 50% of submitted work. Through a combination of AI and human thematic content analysis of student chat logs, we found that in 18.6% of prompts, students asked ChatGPT to write for them. The rest of the prompts involved work leading up to or in support of the writing process. Human thematic content analysis of papers showed that students used ChatGPT to generate 8.2% of the writing they submitted. The most common rhetorical purpose of the AI-generated text they included was discussion/analysis/synthesis. English as a foreign language students (EFLs) in the sample prompted ChatGPT to clarify understanding less often than non-EFLs and integrated less AI-generated text into their papers, with a particularly notable difference in their use of AI-generated summaries. This unexpected finding merits further research, but it suggests that EFLs may use GAI for somewhat different purposes than non-EFL peers.