Timeline for Looking for realistic applications of the average and instantaneous rate of change
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2016 at 18:25 | comment | added | Markus Dittrich | @vonbrand: I know, I know. You're instantaneous speed might be important in this context, but it's not important for you being able to calculate it. That's the point: I want the students to get an idea why anyone in the real world would want to do the same thing they're about to do (1. modelling 2. calculating the rate(s) of change) | |
| Jan 9, 2016 at 18:17 | comment | added | vonbrand | @MarkusDittrich, each time I travel by car the time taken by the trip is important. If my instantaneous speed is to high, I might get a speeding ticket | |
| Jan 9, 2016 at 18:12 | comment | added | Markus Dittrich | @vonbrand: of course something like this would be possible (Although using the steepness of a mountains silhouette for explaining what a rate of change is seems to be somewhat more intuitive). But the question remains: When is calculating something like this really necessary? | |
| Jan 9, 2016 at 5:46 | answer | added | user1815 | timeline score: 5 | |
| Jan 8, 2016 at 20:02 | answer | added | yoniLavi | timeline score: 1 | |
| Jan 8, 2016 at 14:08 | comment | added | vonbrand | Why a mountain, and not just a trip by car from A to B? Mean speed is simple to compute, instantaneous speed is given by the speedometer. Can even mix in direction, if it is a curvy road... | |
| Jan 8, 2016 at 13:52 | answer | added | Ieuan Stanley | timeline score: 6 | |
| Jan 8, 2016 at 13:11 | comment | added | ncr | I think something involving climate change with historical data could be of interest. The are some data sets here, for example: sustainabilitymath.org/PfaffCalc.html | |
| Jan 8, 2016 at 13:06 | history | edited | Markus Dittrich |
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| Jan 8, 2016 at 10:59 | comment | added | Markus Dittrich | Example: The data for the population size of the US from 1900 to 2000 could be modeled by f(t)=t^2 (Let's just assume this would be realistic for simplicity's sake) whereas "t" stands for the years since 1900. All I had to do, to calculate the value for the year 2015 was to insert 115 for t and I'd be done, wouldn't I? If this is the case I'll have a hard time explaining why we need to learn about the rate of change. | |
| Jan 8, 2016 at 10:58 | comment | added | Markus Dittrich | @Aeryk I also thought about using such an example. The problem is, that I actually wasn't able to find out why both growth over a period and instantaneous growth would be of interest to us. I know this sounds silly, but if my goal was to predict the future population size from existing data I would be done after modeling the function that describes the existing set of data, since all I had to do was to insert the year I want to predict for t. | |
| Jan 8, 2016 at 7:03 | comment | added | Aeryk | How about population models where both growth over a period and instantaneous growth are of interest? | |
| Jan 8, 2016 at 0:57 | history | edited | Markus Dittrich | CC BY-SA 3.0 |
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| Jan 8, 2016 at 0:38 | review | First posts | |||
| Jan 8, 2016 at 5:19 | |||||
| Jan 8, 2016 at 0:35 | history | asked | Markus Dittrich | CC BY-SA 3.0 |