The breathing feedback loop

You will write a model of the feedback loop of breathing. The carbon dioxide starts high, the rate of breathing rises, and the extra breaths wash carbon dioxide out.

The idea. The rate is 12 breaths a minute at a pCO$_2$ of 40 mm Hg, and it rises by 1.5 breaths a minute for each 1 mm Hg above 40. In each minute, the pCO$_2$ falls by 0.1 mm Hg for each breath above 12.

Your tasks.

1. Finish rate_for. It gives the rate of breathing from the pCO$_2$.
2. Finish one_minute. It gives the pCO$_2$ after one minute.
3. Set minutes to the number of minutes until the pCO$_2$ is $41$ mm Hg or less, starting from start.