Example meaningful function that is product of two other functions

[hassman]

What could be a real-life example (so no imaginary units and stuff ) 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
and
Taxes owned on (income) = income * 0.34

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

So could someone help me? :shy:

 

[qntty]

What could be a real-life example (so no imaginary units and stuff )

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

 

[HallsofIvy]

Area of a rectangle in which the lengths of the sides are changing with time was the first thing that came to my mind.

 

[matt grime]

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

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.

 

[hassman]

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.