QuestionFind the horizontal asymptote of the Michaelis-Menten equation for chymotrypsin: $v=\frac{0.17[\mathrm{~S}]}{0.021+[\mathrm{S}]}$ .

Studdy Solution

STEP 1

Assumptions1. The Michaelis-Menten equation is given by $v=\frac{0.17[\mathrm{~}]}{0.021+[\mathrm{}]}$ . The rate $v$ of an enzymatic reaction is a function of the concentration [] of a substrate $$.
3. We are asked to find the horizontal asymptote of the graph of $v$.

STEP 2

The horizontal asymptote of a function can be found by examining the behavior of the function as $x$ (or in this case, []) approaches infinity.

STEP 3

To find the horizontal asymptote of the given function, we need to calculate the limit as [] approaches infinity.
$\lim{{[\mathrm{}] \to \infty}} \frac{0.17[\mathrm{~}]}{0.021+[\mathrm{}]}$

STEP 4

We can simplify the limit by dividing the numerator and the denominator by [].
$\lim{{[\mathrm{}] \to \infty}} \frac{0.17}{0.021/[\mathrm{}]+1}$

STEP 5

As [] approaches infinity, the term $0.021/[\mathrm{}]$ approaches0.
$\lim{{[\mathrm{}] \to \infty}} \frac{0.17}{0+1} =0.17$ The horizontal asymptote of the graph of $v$ is $0.17$ .

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