Example meaningful function that is product of two other functions

In summary, the product of two elementary functions of one random variable may have a meaningful interpretation in real life. For example, the function that maps monthly income to days one can live off it and the function that maps monthly income to taxes owed on that income. However, their product, taxes times days, may not have an obvious or practical meaning to the average person. Other examples of meaningful interpretations could include the weight of a meteor at a certain time or the area of a rectangle with changing side lengths. While the product of taxes and days may not have a clear purpose in everyday life, it does not mean it is useless and could potentially have a useful application in certain scenarios.
  • #1
hassman
36
0
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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  • #2
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
 
  • #3
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
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.
 
  • #5
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.
 

Related to Example meaningful function that is product of two other functions

1. What is a meaningful function?

A meaningful function is a mathematical expression that represents a real-world relationship or phenomenon. It can be used to model and predict outcomes in various scenarios.

2. What do you mean by "product of two other functions"?

In mathematics, the product of two functions refers to the result of multiplying the output of one function by the output of another function. This can be written as f(x) * g(x) or f(x)g(x).

3. Can you provide an example of a meaningful function that is a product of two other functions?

One example is the logistic function, which is commonly used to model growth or decay in biology and economics. It is the product of the exponential function and the reciprocal function (1 + e^-x)^-1.

4. What are the benefits of using a meaningful function that is a product of two other functions?

Using a meaningful function that is a product of two other functions allows for a more accurate representation of complex relationships. It also allows for more flexibility in adjusting the function to fit different data sets or scenarios.

5. How can meaningful functions that are products of two other functions be applied in real life?

These types of functions can be applied in various fields such as finance, biology, physics, and engineering. They can be used to model population growth, predict stock market trends, analyze chemical reactions, and more.

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