It would help if you didn't keep misinterpreting what I say. It would also help if you paid more attention to your physics and maths classes as you seem to lack basic knowledge.
Do not worry about my Physics and Mathematics classes.
(1) I spoke of an exponential function in the way anyone who has studied science is speaking – i.e. a function involving an exponential. That, of course, extents beyond the basic exp(x). For example y=A*exp(b*x)+c is an exponential function.
There, it is clearer, you nuance your words.
When we speak about the exponential function, the one who occurs us naturally it is f(x) = e^x.
How wanted you that I guess that you speak about a function which
involving an exponential ? Sorry if I badly interpreted your words, but your message was ambiguous.
If you didn't know this then perhaps your knowledge on the matter is "google level" where you just googled "What is exponential function?" and got back e^x.
The "google level" is not very appropriate, sorry.
Also bear in mind that if x has units that are cancelled out by b, the constant A will introduce the units back of whatever you are calculating.
Yes I know. For example, if the variable x expresses himself in second (dimension of time: T), then the dimension of variable b will be 1/T that is there T^(-1).
Also remember that y and x don't need to have the same units.
Yes.
(2) What I use as the independent variable, x, is not the strength or the speed or whatever, but the battle power level. In other words the strength or speed, y, is an exponential function (or at least some other non-linear function with constantly positive gradient) of the power level, x. Not the other way around. Also for all intents and purposes battle power levels can be unitless to begin with and even if they weren’t see point (1) above. If you still don't get it you may consult the following Youtube video:
You said that the power level measured by scooter can be without units ??
I saw the video, the reasoning is good but I doubt hardly that Akira Toriyama is to break with any function mathematics to say that the relation between power of fight and physical abilities is not linear.
When we were reflected, the story indicated that Kaioken multiplies the strength of fight by two and Kaio explained that the same Kaioken could allow Goku to double his power. Thus according to the manga, have twice more units involve to be twice as powerful (if I do not a mistake).
(3) The overall relationship governing the actual strength (y) and power levels (x) may well be piece-wise as well, i.e. have different functions within different domains (probably 100fold ones for simplicity). For example:
y=f1(x) for 5 ≤x<500
y=f2(x) for 500 ≤x<50K
y=f3(x) for 50K ≤x<5M
and so on
The above will allow for a highly exponential function within the first range where you can go from human level (PL=5) to moon busting level (PL=500) (an increase in destructive capacity by a 100 septillion times) but for a less exponential one for the next 100fold increase in power level (where you only get a mere 1000x increase in destructive capacity - moon level to Earth level).
The problem it is because in the manga there is a lot of incoherence of genre. You know, as I told it to you, I do not think that Toriyama is to complicate the life to calculate the necessary heat or kinetic energy to destroy the moon with Kamehameha or of a simple punch.
It in had to make that for the feeling, Dragon Ball is a manga which aims at a readership of young teenager which are not all capable of understanding the physical and mathematical notions which you use.
I do not say that your way of arguing is false, quite the opposite, she is logical, you have a good scientific approach, but I think that we cannot unfortunately apply the laws of physics to calculate the power of the heroes. Because Dragon Ball is a manga of science fiction, that is not the reality. It is incomparable.
I think that I am going to stop here, because like that was said higher, this kind of discussion is a waste of time. I do not say that against you Speedster, I say simply that we complicate things for not much.
Peace be upon you.