What do you mean when you say something a change is exponential?
I know what it means in mathematics, but I realized recently people use it to mean different things.
1. Some people just use it to mean “a big change.”
2. Some people use it to mean “anything not linear.” I.e. with an exponent.
3. In mathematics, its a very specific functional form.
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I use the word to describe a large change, like “My increase in strength after I started taking steroids was exponential”.
Well if take a number and you square it, the two is the exponent. So if you take 2 and you square it, the exponent is 2 and the result is 4….which means for every 2 of something you’ll get 4 of another and for every 4 of something you’ll get 16 of the other and that is not a linear change, that is an exponential change.
I take it to mean that when one thing changes, it makes a bunch of other things change too, therefore the first change is exponential because one change begets many changes and the whole initial change becomes much bigger than it’s original state of change.
It’s kind of like that old ad on TV where the woman was talking about her shampoo and then she says, “First I told two people, and they told two people, and then those people each told two people.” The number of people who end up knowing about the shampoo is much greater than if the first person just told one person and each subsequent person only told one other person.
Changes produce more changes, which in turn produces more changes… and on and on and on.
I use it to refer to phenomena which I think, when graphed, would show a sudden, steep upwards curve.
It has a technical meaning but I think it is often used to mean simply ‘out of control’.
Wow… okay, thanks. I always used it to mean the technical meaning and got very confused when people used it to mean other things.
@Simone_De_Beauvoir I found out that people use it that way a little while ago which is what prompted me to post this question. Technically, what you are talking about is not “exponential” but “quadratic.” In exponential things, the exponent is not a constant but is the variable.
So x^2 is quadratic and we get 2 > 4, 3—> 9, 4—> 16, 5> 25, etc…
But 2^x is exponential and we get 2—> 4, 3—>8, 4—> 16, 5—> 32, etc…
From there on, 2^x grows MUCH faster than x^2. If I could post pictures here this would be easier to show but you can also see it in excel…
@Kardamom What you are saying is essentially the technical definition. The number of people who knows keeps doubling.
Anyway, thanks folks. This helped clear up my confusion.
@roundsquare Yes, a quadratic is one type of an exponential equation, I thought.
Exponential growth of microorganisms. It takes time x to double their numbers. You can also watch water lilies on a lake.
@mattbrowne Ah yes, I see. Didn’t make the connection :)
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