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[–] 29 points 1 year ago (3 children)

It’s really a term from statistics. It’s the same as an exponential growth rate, but you only take the value of the exponential function at discrete intervals.

If you had a function you wanted to graph like 2^x^, exponential growth is like saying x can be any real number (even a fraction or something) and every part of the line you draw is counted, but geometric growth would be a discrete value for x like [1, 2, 3, …, n] where x is from that interval pattern. It’s useful in statistics for measuring data based on something like time. The examples I was taught were like cells splitting in two at a fixed time interval. You can still draw the graph like it’s a single curve to visualize it, but the actual data points are at discrete values for x and just not in between.

I haven’t had a stats or math class in a long time, but I believe this is correct enough from a quick scan of Wikipedia.

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  • [–] 3 points 1 year ago (2 children)

    Yeah, that's basically how I remember it, though it's not always stats--the terms are used in other fields of math as well. A first calculus class typically includes a proof that the limit of the sum of an infinite geometric series (a + ar + ar^2 + ar^3 + ...) tends towards a/(1-r) where a is the first term and r is the ratio of successive terms, provided that -1 < r < 1. (Otherwise the series diverges and the limit isn't defined.)

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  • [–] 2 points 1 year ago (1 child)

    Absolutely! I vaguely remember a discussion of geometric growth in at least one other course, but I was doing my best to give a thorough layperson’s explanation without getting into more analytic definitions for geometric series or the concept of continuity. I studied abstract/theoretical mathematics in my undergraduate degree, so I only really remember seeing geometric growth defined in statistics courses as far as applied mathematics goes as I avoided those courses where I could. I’m not in academia, and I did not pursue a further degree, so my apologies if I wasn’t entirely accurate. My mathematical theory is very rusty these days. lol

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