Final answer:
The alarm-initiating device that is activated by a rise in temperature of 12°F to 15°F in one minute is the Rate-of-rise heat detector.
Step-by-step explanation:
The alarm-initiating device that is activated by a rise in temperature of 12°F to 15°F in one minute is the Rate-of-rise heat detector. This detector is designed to detect rapid increases in temperature, such as those caused by a fire. When the temperature rises above the set threshold within a short period of time, the detector triggers an alarm.