Dynamic capacity provisioning is a useful technique for handling the multi-time-scale variations seen in Internet workloads. In this paper, we propose a novel dynamic provisioning technique for multi-tier Internet applications that employs (i) a flexible queuing model to determine how much resources to allocate to each tier of the application, and (ii) a combination of predictive and reactive methods that determine when to provision these resources, both at large and small time scales. We propose a virtual machine-based technique that reduces server switching overheads and enables efficient implementation of our provisioning technique. Our experiments on a forty-machine Linux-based hosting platform demonstrate the responsiveness of our technique in handling dynamic workloads. In one scenario where a flash crowd caused the workload of a three-tier application to double, our technique was able to double the application capacity within five minutes, thus maintaining response time targets. Our technique also reduced the overhead of switching servers across applications from several minutes to less than a second, while meeting the performance targets of residual sessions.