Second Degree Polynomial and Other Models

For users of the Mathcad browser: wmc-rp1.mcd (9 KB, ver. 5.0)

The drying time of varnish depends on the amount of a certain chemical additive it contains.

m/g 1 2 3 4 5 6 7 8
t/h 7.2 6.7 4.7 3.7 4.7 4.2 5.2 5.7

The experimental data for the drying time vs. mass of additive shows a parabolic trend. Determine the a, b and c constants that would fit the formula: Formula:  y=cx^2+bx+a. This type of problem in Mathcad can be handled by the built in function linfit . The input for the experimental data are in the usual vector form, and then a function of the type is defined. The values of the constants can then be simply obtained by typing linfit(x,y,F)=
It is apparent this can be applied to any other function that can be written as a sum of powers of x, such as etc.

The amount of additive for which the drying time can be expected to be minimum is obtanied from the first derivative of the function which would be: y'=2cx+b, or for y'=0, x=b/2c.
The expected drying time of a varnish when, for example 6.5 g of active supstance are added, is simply t=c*(6.5)^2 + b*6.5 + a, or in this case, 4 h and 20 min.
On the other hand, if we want to find the amount of additive necessary to make a varnish that dries in 5 hours, either the Root, or the Given/Find function can be used.
The earlier DOS version of Mathcad does not have the linfit function, and the parabola problem can be solved by introducing the individual statistical functions in a Given/Find block.


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