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:
.
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:
The expected drying time
of a varnish when, for example 6.5 g of active supstance are added, is
simply
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.