QuestionFind the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: . What does it signify?
Studdy Solution
STEP 1
Assumptions1. The Michaelis-Menten equation is given by . We are asked to find the horizontal asymptote of the graph of .
STEP 2
The horizontal asymptote of a rational function can be found by looking at the degrees of the numerator and denominator.If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is .
If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients.
If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
STEP 3
In our case, the degrees of the numerator and denominator are equal (both are1), so the horizontal asymptote is the ratio of the leading coefficients.
STEP 4
The leading coefficient of the numerator is0.17 and the leading coefficient of the denominator is1. Therefore, the horizontal asymptote is The significance of this is that as the concentration [] increases, the enzymatic reaction rate will approach0.17. This is because the horizontal asymptote represents the limit of the function as [] approaches infinity.
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