# Example meaningful function that is product of two other functions

1. May 28, 2009

### 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 :yuck:

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

So could someone help me? :shy:

2. May 28, 2009

### qntty

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

3. May 29, 2009

### HallsofIvy

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

4. May 29, 2009

### matt grime

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.

5. May 29, 2009

### hassman

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.