As an astronomy buff, I can offer the size of a star vs. the lifetime of a star as an example of something which as input increases, output decreases:

Our sun should burn for about 10 billion years (and we're about halfway there), but a star 10 times more massive will burn about 3,000 times brighter and live only about 20-25 million years. I'm not sure of the exact big-O or little-o equations, but astronomers have known this for some time: more massive stars burn exponentially brighter (and therefore live much less time) than smaller stars.