Example meaningful function that is product of two other functions

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Discussion Overview

The discussion revolves around finding real-life examples where the product of two elementary functions of a single variable has a meaningful interpretation. Participants explore various scenarios and functions, considering both practical applications and theoretical implications.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests a function mapping monthly income to the number of days one can live off it and another mapping income to taxes owed, questioning the meaningfulness of their product.
  • Another participant argues that imaginary units can have real-life applications, particularly in physics, and suggests that any two varying quantities can yield a meaningful product.
  • A third participant proposes the area of a rectangle as an example where the lengths of the sides change over time, implying a meaningful interpretation of their product.
  • Further discussion questions the initial claim about the lack of meaning in the product of taxes and days, suggesting that the absence of an obvious interpretation does not render it useless.
  • A participant redefines "meaning" as "useful in average Joe's everyday life" and proposes a scenario involving interest rates and starting capital, seeking a common variable that influences both.

Areas of Agreement / Disagreement

Participants express differing views on the meaningfulness of certain products of functions, with some asserting that a lack of an obvious interpretation does not imply a lack of utility. The discussion remains unresolved regarding specific examples that meet the criteria of meaningfulness.

Contextual Notes

Participants acknowledge the challenge of identifying a common variable that affects both starting capital and interest rates, indicating potential limitations in their examples.

hassman
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What could be a real-life example (so no imaginary units and stuff :approve:) where the product of two elimentary functions of one random variable has a meaningful interpretation.

Let's say I have a function that maps my random monthy income to number of days I can live off it and another function maps the same random monthly income to taxes owned on this income. Like:
Days I can live off (income) = income / 20 :cool:
and
Taxes owned on (income) = income * 0.34

However their product, taxes times days, has no meaning at all. :confused:

So could someone help me? :shy:
 
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hassman said:
What could be a real-life example (so no imaginary units and stuff :approve:)

Imaginary units are plenty useful in real life (ie physics)


Anything that you can multiply together and which can vary can have a real life meaning

m(t) = mass of an object at time t (You can think of some reason why the mass would change, eg maybe its a meteor
a(t) = accelaration at time t (meteor getting closer to a planet?)

(ma)(t) = Weight of meteor at time t
 
Area of a rectangle in which the lengths of the sides are changing with time was the first thing that came to my mind.
 
hassman said:
However their product, taxes times days, has no meaning at all. :confused:

Why does it have no meaning at all? Just because you can't think of an obvious one doesn't mean that it's useless.
 
matt grime said:
Why does it have no meaning at all? Just because you can't think of an obvious one doesn't mean that it's useless.


Perhaps I should substitute "meaning" by "useful in average Joe's everyday life".

Like for example, the value of the function of variable x that gives us the prevailing interest rate multiplied by the value of the function of variable x that gives us the starting capital of average Joe. Their product would be the interest payment that Joe could receive. I just can't think of variable x that both affects Joe's starting capital and interest rates.
 

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