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 2x, 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.
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.)
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
Oh, I only minored in math, I’m no expert either! Yeah, your explanation was really fine, I just thought the “sum of a geometric series” thing might ring a bell for some readers.
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 2x, 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
xlike [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 forxand 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.
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.)
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
Oh, I only minored in math, I’m no expert either! Yeah, your explanation was really fine, I just thought the “sum of a geometric series” thing might ring a bell for some readers.