If you ingest 100mg of caffeine instantly (say, as a pill), then given the six hour half-life of caffeine in the body, you'd calculate the milligrams of caffeine left in your system with $100(\frac{1}{2})^{\frac{t}{6}}$ (where $t$ is the time since ingestion in hours).

What is the equation if you consume the 100mg at a constant rate over the course of an hour (savoring your coffee)?