horbowiec.7527 wrote:This is regarding Biology Chapter 4 Worked Solution Q8 (BIO105):
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 lessthan symbols?
ACER has a graphbased 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 lessthan sign, <<, is presumably an approximation of the idea of "muchlessthan". 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 "muchlessthan" 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).