Timeline for Interesting settings for exponential growth or decay
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9 events
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| Apr 19, 2018 at 18:04 | comment | added | guest | graph 4 is probably the hardest to come up with examples of (e.g. reaction catalyzed by products, looking at the starting material point of view). It corresponds to graph 1 (which is the products view of explosive growth). [Another graph 4 example is the incumbent product market share, e.g. blackberry, as another product I-phone, begins explosive growth. Things look OK for Blackberry at first, minor near term effects, but get bad as the I-phone explodes.] | |
| Apr 19, 2018 at 17:59 | comment | added | guest | I really think you should figure it yourself (some of the learning is from the research), but: a is mostly graph 1, b is type 2 for decay and type 3 for buildup. c is type 2 and 3 (depending on POV, concentrating or diluting). Note the initial and equilbrium levels are likely nonzero. d is 2 charging and 3 discharging. e is generally 3. f is 2 compaction and 3 velocity. g is 2. h is 2. i is all of them (it's a Gaussian curve or parts of it). j same as i. k same as i. [You should draw a Gaussian bell curve and label it with your graphs: 1, 3, 4, 2. A sigmoid is 1, 3.] | |
| Apr 19, 2018 at 17:46 | comment | added | guest | Yeah toxin/drug buildup and removal is a big one also. Any type of concentration with a feed and bleed (salt tank dilution, fish in stream, the very slow chlorine level reduction in upper atmosphere after Freon laws change, etc.) will have these dynamics. I'll take a look at the graphs. | |
| Apr 19, 2018 at 17:34 | comment | added | Chaim | Thanks. Your scientific examples reminded me that I've seen exponential models of the kidney's elimination of drugs from the blood. Looking for that example on the web I found a nice activity at illuminations.nctm.org/lesson.aspx?id=3081. Can you tell me, though, which of your examples would correspond to each of the four graphs I've added to my question? I think most are concave up and decreasing, as positive quantities draw closer to zero. | |
| Apr 19, 2018 at 17:26 | history | edited | guest | CC BY-SA 3.0 |
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| Apr 19, 2018 at 16:42 | history | edited | guest | CC BY-SA 3.0 |
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| Apr 19, 2018 at 15:54 | history | answered | guest | CC BY-SA 3.0 |