0

I have the following situation.

I have an start point of 40 degrees temperature and endpoint of 69 degrees.

Now i want to normalize all values in this range into an skala from 1-15.

This should happen exponentally. I already have a formular based on an linear approach, but i want the number between 1-15 rise exponentally the more the temperatures comes to the endpoint 69. 

Example: 40 degrees = 0P
         51 degrees = 4P
         61 degrees = 12P

Could you point me out to the right direction. I dont know why but i am having a mind blockade at the moment ^^

Thank you in advance!

gammatester
  • 18,827
Ryo Saeba
  • 13

1 Answers1

0

First normalize by subtracting by $39$... This assures we can work with an Exponential. We also subtract $1$ from the Scala... This gives us $x^0 = 1$ as we need, so interrogating for only one value is needed

$1$ degrees = $ 0$
$30$ degrees = $ 14$
This implies that $x^{14} = 30 \implies x \approx 1.275$
You will now need to get your data points from that curve, not the other way around. In general, you have the function $1.275^{x-1} + 39 = y$, where $y$ is the temperature in degrees and $x$ is the Scala value

Brevan Ellefsen
  • 14,793
  • First thank you. That sounds good. That means now i only need to adjust this formula, so i have x = (term), because i need the scale value, not y the temperature.. – Ryo Saeba Jun 08 '16 at 13:53
  • @RyoSaeba indeed. Notice my edit... I'm sorry for the confusion, I must be tired because this post went through multiple rewrites... Never been so bad at math in my life XD with my corrected answer, just subtract 39 from both sides, take the logarithm base 1.275, and add 1. Note that you can also directly use the 14th root of 30 of you want to be exact with your scale – Brevan Ellefsen Jun 08 '16 at 13:58
  • i have just tested this, but i dot get the results.. am i missing somthing.. the formula resolved for x is x = ln(y-39) + 1 .. Now i put temperature values for y to check for the scala points.. If i enter 40 i get 1.6 as an x. Seems okay. If i enter 55 (which should be critical high) i get 2.77 .. shouldn this be around 12, 13 points... oh my it seems i am tired too – Ryo Saeba Jun 08 '16 at 14:28
  • @RyoSaeba well, without looking too much at it, I would note that you are using the natural logarithm, while you should be using base 1.275 – Brevan Ellefsen Jun 08 '16 at 14:31
  • @RyoSaeba I'll look at it more later, but I spent enough time correcting this earlier XD I'm late for work already. – Brevan Ellefsen Jun 08 '16 at 14:32
  • I do note that you aren't using this correctly, even if you are using the natural logarithm... Note that if you plug in 40 for y you get 1, as ln(1)=0 – Brevan Ellefsen Jun 08 '16 at 14:36
  • Thanks.. you must be right . I will look into this again. I will mark you as an answer, thank you for your effort! – Ryo Saeba Jun 09 '16 at 05:29