This is happens with the temperature of water when you drop a hot stone in it.
The model is a combination of logistic functions.
The dotted lines are 'worst case scenarios' based upon the precision of the measurements and the error propagation through the model.

Are you a science teacher? A student? A researcher? An engineer?

Then, sooner or later you will need software to find a pattern in your measurements!

For example: y=ax+b, y=asin(bx+c)+d, y=ba^x+c, etc.
You enter your measurements (x_i,y_i) and this program finds the parameters a, b, c...

Many programs do this, but this one is easy to use, more correct and not expensive (25€/licence)!,
and I can assist you personally.

Strong features:

• It works with iteration, which is applicable to any kind of function and often more precise because there is no need to take logarithms of variables.
  
  
• The weights of the data points are taken into account, using the standard deviations (confidence intervals/measuring errors) of both x and y variables! They are also used to make a realistic estimation of the parameter confidence intervals.
  
  
• Easy to use: you can visually follow the iteration proces, and that can give you a lot of insight in the stability of the parameters! This makes it interesting to show in a classroom!
  
  
• Model functions in this version: constant, linear, quadratic, cubic, exponential, 1-exp, Gauss, double Gauss, power, logistic, double logistic (peak), sine, double sine, damped sine, parallax, rational (Michaelis-Menten), refractive index. Being an experimental physicist, I have personally tested every model with real world data. These are included for educational purposes.
  I will add more model functions according to your needs! And since this is version 1.0, you will get some free updates for a while!
  
  
• Normally, the model parameters are optimized by minimizing the sum of the squares of the predicted minus the observed y values. This is called 'Ordinary Least Squares fitting'. This works reasonably well in case the data don't have much noise.
  Unique in this program: in the case of invertible model functions, the fitting can be done in x and y directions, which gives a dramatical improvement! I call this 'multidirectional regression' (not to be confused with 'total least squares' or 'Deming/orthogonal regression'). Especially for power function models with noisy data (e.g. biometric data) my program produces way better results than other well known software (e.g. Wolfram, GraphPad Prism, GeoGebra, Graphmatica, TI-84, NCSS,...)! Don't believe me, just try it!
  
  

Ordinary and multidirectional fitting applied to mass vs height data of adult men with fat% between 11.6 and 13.8, showing that the BMI should be closer to m/h³ than to m/h².

Screenshot:

The first version of this software program is released the 10th of April, 2021. Current version: 1.1 (14th of July 2021)

Requirements: pc with Windows 7 or later/Mac with Windows emulator; recommended screen resolution: 1920x1080 (full HD).

Author: Koen Van de moortel - info@lerenisplezant.be - +32 9 2277036 or +32 47 7368526 - Presentation on Youtube

Support: Fire your questions & requests! I'm not sure if I can answer all of them, but I'll try! - User discussion forum

Main page - Private math tutoring

BTW: "Leren is plezant" is flemish for "Learning is pleasant".