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I am doing a Science outreach project on Mathematics.

I want make mathematics more interesting for students, since only when they realize its' beauty and useful in real world applications, they will learn mathematics in a more active manner.

But one student asked me:" Now we have a question related to formula type as $e^x + ax^2 +bx$. What is the meaning of this type of mathematical formula in the real world? Why it is important that we should figure out to solve it?"

So I am wondering whether there is a such database that we can find real world application for a specific type of formula, or at least close to it. For example, is this $e^x + ax^2 +bx$ type of formula related to something in physics, chemistry, biology, mechanism, industry and agriculture?

Hope you can give me some afflatus on this type of question!

Thanks!

Dexter
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    Is $e^x + ax^2 + bx$ really a formula you are using in your teaching? Maybe you should be looking for more beautiful and useful formulas. – David K Jun 29 '21 at 11:55
  • Finding such a database may not be easy but you may select mathematicians presenting things in a nice geometrical way. Vladimir Arnol'd for example introduces ODEs with rather simple equations and uses for example predator-preys models that may appeal to imagination. – Raymond Manzoni Jun 29 '21 at 12:35
  • It looks like your $e^x+ax^2+bx$ formula looks like this graph which looks useful. Any function can be used to model a way of organization as there is an input “getting organized” into the output. – Тyma Gaidash Jun 29 '21 at 13:37
  • @DavidK, this is just a question one student just happened to find on his exam, then we got this idea to try to find its possible application in the real world. – Dexter Jun 30 '21 at 01:29
  • @TymaGaidash Thanks so much for your beautiful graph, I also tried it on some software such as mathematics. It did make abstract formula visualized. – Dexter Jun 30 '21 at 01:31
  • @RaymondManzoni, Thanks so much for your recommendation about this book, I will try to read it. Maybe such a database really needs some guys familiar with math, physics, chemistry, industry, etc,. and collect all formula and equations exist in various scientific and technical fields such as in all books. It is really a hard work, maybe in the future some AI may help us search formula and equation in all books. – Dexter Jun 30 '21 at 01:35
  • Glad this interested you @Dexter. Note that restraining your quest to more specific subjects like exponential or polynomials may return some interesting discussions like about e or polynomial factorization or Fourier series (the "Related" links at the right may also be of interest). Excellent continuation anyway, – Raymond Manzoni Jun 30 '21 at 06:25
  • @RaymondManzoni Thanks so much for your kindly remind, this may be a good idea to discuss this expression in separated forms. – Dexter Jul 04 '21 at 05:55

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