Um, ok. Your position baffles me, because you clearly understand what exponential means mathematically, yet you insist that the word means something else colloq

Um, ok. Your position baffles me, because you clearly understand what exponential means mathematically, yet you insist that the word means something else colloquially. Specifically "faster than linear". Usually, people who (mathematically) misuse the term do so because they don't understand what it actually means, but that's not what is happening here. If it's going to mean something precise, such as > The slope of the derivative is positive and linear. then why not pick the precise thing that the word already means? Is x*log(x) also exponential to you? If so, then why not use the word that already exists: superlinear? If not... oh wait, the above definition I quoted wouldn't even cover x^2, since the slope of its derivative is constant, not linear. So I'm just completely confused; I can't figure out which (mathematically) non-exponential functions you would like to label as exponential. x*1000, no. x^3, yes. x^2, I don't know. x*log(x), I don't know. x^2*log(x), I don't know. > "Exponential" in the colloquial sense means that the derivative has a positive slope. "Exponential" in the colloquial sense means that the speaker isn't using a mathematical sense, and so isn't considering first or second derivatives. I don't buy the argument that the colloquial sense accepts x^3 and rejects x^2, and in fact I bet I could find someone using it for a linear relation ("My workload has gone up exponentially since you laid off half the team!") > "Exponential" in the mathematical sense, means the derivative is a function of x. No it doesn't. x^2 is not mathematically exponential, yet its derivative is a function of x. Exponential means the derivative is exponential. But that's just a detail that doesn't really change the core of your message. The main purpose of the mathematical definition is to exclude polynomials. The main purpose of the colloquial definition seems to be something like an impressive or important increase.