The real reason that the battery use is poorer in weak signal areas has not been properly addressed.
When you/the cellphone is in a weak area, the Radio Transmitter in the phone has to greatly increase the Strength of its' output signal (more power).
Cellphone radios transmit power is governed by signal strength. If the cellsite is close and very strong, the phone transmit power is decreased to the absolute minimum required to be heard at the cellsite.
If the signal is poor, the phone's transmit power is ramped up to the maximum it can provide. That can easily run multiple values of battery use compared to a full signal.
so, if you live or work in a poor signal area, you will experience worse than normal battery use.
I live in a strong area, as I have a Network Extender in my home. (cell sites are very weak for me, so I bought a cell site Network Extender)
When I go to work though, which is in a very rural area and deep down in wooded ravines, etc... I notice my battery percent drops faster than it does at home.