Under what conditions would the breathing rate increase?

The breathing rate is defined as the number of breaths a person takes during a one-minute period of time while at rest. ​
On an average, a healthy human breathes 12-16 times/minute.​ ​
There are many causes of an increased breathing rate.
The more common causes are:​ Respiratory rates normally increase during exercise.​
If the oxygen level in the blood is low, or if the carbon dioxide level in the blood is high, breathing rate increases.

1. At high altitude there is lower air pressure compared to a lower altitude or sea-level altitude so the partial pressure of oxygen in the air is lower, and less oxygen is breathed in with every breath.
Hence to increase the oxygen level, breathing rate increases.​

2. Dehydration, fever or severe infection increases the rate of breathing.