why we do things in math?

>>8619276
Usually a field has two defined operations. Then you can prove that other operations follow from them.

For example the reals have two operations, addition and multiication. You can use the trichotomy law to get division and subtraction. You use multiplication to get to exponent, etc.....

The logic behind it is that you unfurl definitions to more and more basic logic until you get back where you started.

>>8619276
>when I see formulas an there is a exponential, why?
Because we want to.

>how do you know you have to elevate something to a determined power?
We know this if when we simulate solving the problem in our mind, at the end we get a solution.

> there is logic at the bottom of mathematical operations and formulas, but I can't see it

There isn't much logic to it. For every problem there are a billion ways to solve it so you just need to start simulating solving it in your brain until something clicks. Then you write that down.

>how do I undertand this kind of things?
By solving problems.

An exponential basically implies a dependence of the variable or physical observable upon itself. i.e. the bigger it is the bigger it wil get.

>>8619276
You're accerating at 5m/s^2
You travel from rest for 5s
How far did you go?

>>8621022
How do i know if i went in a straight line the whole time?

>>8621022
Assuming it is a straight line and it's just normal phisycs (I hope) less than 1,5 milimeters?