AI-powered software development tooling is changing the way that developers interact with tools and write code. However, the ability for AI to truly transform software development may depend on developers' levels of trust in these tools, which has consequences for tool adoption and repeated usage. In this work, we take a mixed-methods approach to measure the factors that influence developers' trust in AI-powered code completion. We found that characteristics about the AI suggestion itself (e.g., the quality of the suggestion), the developer interacting with the suggestion (e.g., their expertise in a language), and the context of the development work (e.g., was the suggestion in a test file) all influenced acceptance rates of AI-powered code suggestions. Based on these findings we propose a number of recommendations for the design of AI-powered development tools to improve trust.