Environmental Engineering Reference
In-Depth Information
cðtÞ¼c 0 exp
ð l
(10.2)
There are two parameters: the initial concentration c 0 and the decay constant
.
Note that the fitting procedure can be performed for any dependent variable c and
the independent variable t ; both symbols do not necessarily represent concentration
and time in this chapter.
As the polyfit command works with polynomials, one may use the idea that the
exponential curve is a linear curve in logarithmic representation. Thus the polyfit
command can be used for the logarithm of the concentration vector:
l
p = polyfit(tfit,log(cfit),1)
p =
-0.2619 -0.3387
The best fit for the logarithm is thus given by:
log
ðcÞ¼
0
:
2619 t
0
:
3387
(10.3)
or:
cðtÞ¼
exp
ð
0
:
3387
Þ
exp
ð
0
:
2619 t
Þ
(10.4)
¼
0
:
7127 exp
ð
0
:
2619 t
Þ
Comparison with formula ( 10.2 ) shows that the second line of ( 10.4 ) is the aimed
formulation with c 0 ¼
0.8236 and
l ¼
0.3487. In Fig. 10.4 the result is again
plotted together with the original data:
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
Fig. 10.4 Exponential fit for example batch experiment
 
Search WWH ::




Custom Search