Explain the physics of electron-positron annihilation that occurs inside the patient's body and how it allows the PET scanner to locate areas of high tracer concentration.

The half-life of oxygen-15 is 122 s. Calculate the time $t$, in seconds, required for the activity of the oxygen-15 radiopharmaceutical to decrease to 15% of its initial value.

Suggest why a hospital performing PET scans with oxygen-15 must have a cyclotron (particle accelerator) located very nearby.