Crimes against nerdity

I just can't take it any more! The time has come for me to take a stand, to right a wrong, to speak out where there has been silence. Criminals are a cowardly and superstitious lot. In brightest day, in blackest night etc etc. I can no longer stand by while my lecturers describe curves as "exponential" when they merely have a positive second derivative. I know you're with me on this one.

Today it happened again. That makes twice this semester, and at least twice last semester. Today's curve described the ventilation/perfusion ratio of the lung. We were shown a graph of ventilation (litres per minute) versus distance from the base of the lung. The graph was a linear one, so y1 = ax+b. On the same graph was shown perfusion, again of the form y2 = cx+d. The ventilation/perfusion ratio was then shown and was described as being exponentially increasing. But if you let x = (z-d)/c, it's easy to see that (ax+b)/(cx+d) = a/c + (b - ad/c)/z, which is clearly a hyperbola! Outrageous!

If you think it's unimportant, consider the difference in the two cases as the size of your lungs approaches infinity!

Similarly, we were previously shown another example which was two linear curves multiplied together. Thus, it was simply a polynomial rather than exponential! How would you feel if you were a patient lying in hospital struggling for breath and you heard one of your treating physicians so egregiously confuse his high-school mathematics?

Every time it happens I feel like sticking my hand up and correcting them but part of my brain (I'm guessing the right hemisphere) tells me to be quiet. It is innate knowledge amongst medical students that any consultant that is corrected by a student would tear that student limb from stinking limb and I have no desire to be dismembered just yet. Nevertheless, ignorance breeds where wise men say nothing. If you are reading this I place upon you a most solemn duty. The next time a lecturer describes a curve as "exponential", you must raise your hand and enquire whether the gradient of the curve is proportional to its height or if it merely curves upward. And don't tell them I sent you.