Example 1: Hop growth

Hops, which are required for the production of beer, are a fast growing creeper. In order to make statements about hop growth, the following series of measurements was taken during an investigation.

Time t (in weeks)02468101216
Height (in m) 0.61.22.03.34.15.05.55.8

(Example from Lambacher Schweizer: Leistungskurs Analysis, Edition Baden-Wuerttemberg, 1st edition 2000)
 

Data from:  "hopfenwachstum.csv"

Saturation limit:  6
     Dark figure:  1

f(t) = 4,0189/(0,66981 + 5,3302*e^(-0,3562*t))

Inflection point W(5,8226/3)

Maximum growth rate f'(xw) = 0,53433

8 Values 
Coeff.of determin. = 0,99383916
Correlation coeff. = 0,99691482
Standard deviation = 0,16172584

As in the book, the value 6 was assumed as the saturation limit. Nevertheless, the results differ from those of the template. However, no curve fitting is carried out there, but the proportionality factor k  is calculated using an arbitrary data pair, for example with  ( 12 | 5.5 ). The data for this example are stored in the file hopfenwachstum.csv .