horbowiec.7527 wrote:This is regarding Biology Chapter 4 Worked Solution Q8 (BIO-105):
Could you please explain why exactly you made this simplification: "simplifying it further by concluding that if [S] << Km then [S] + Km is approximately equal to Km"?
Mathematically if S = 4 and Km = 5 then yes S << Km but S+Km = 5+4=9 which is not approx = 5 (Km).
Mathematically, your example of S = 4 and Km = 5 is reasonable if the information provided was that S < Km. But why put 2 less-than symbols?
ACER has a graph-based unit where, for concentration, they provide no numbers and no explanation for these 3 symbols:
-
+
++
So, presented with this ambiguity, you are almost forced to deduce that the symbols mean, respectively, little or no concentration, elevated concentration, and very very high concentration.
Similarly, the double less-than sign, <<, is presumably an approximation of the idea of "much-less-than". Now you might argue: how do I know if it is so much less than Km that the effect on the denominator becomes negligible? The hint is that the slope seems to be coming from [S] of zero or so close to zero that it is impossible to discern. Thus, either using the "much-less-than" expression provided or the graph, we can feel confident that [S] is closer to zero than it is to Km.
Alternate for BioMed students: It is not necessary to use assumed knowledge, but some students might recognize Km as the 1/2 maximum substrate concentration (graph in BIO 4.3), and thus notice the big difference between Km and where the slope begins (so close to zero).