anonymous
  • anonymous
W- Lambert function
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
abb0t
  • abb0t
U ok? If it's a medical emergency, dial 9-1-1.
anonymous
  • anonymous
I want to ask u about how to derive the 3rd Equation (On picture below), becomes the4th equation (on picture below) by using W-Lambert function ???
abb0t
  • abb0t
I used to know this when I took an enzyme kinetics course and this derivation is long. About half a page - 1 page typed out.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

abb0t
  • abb0t
Maybe you can read about it on the article you found it on? http://mvputz.iqstorm.ro/upload/LogisticEnzymeKinetics_Paper1.pdf
abb0t
  • abb0t
It's a good paper :)
anonymous
  • anonymous
i have been reading this paper, and I did not find what i want.., would u kindly help me?? do you still have a reference about this derivation (complete with W-Lambert function)
abb0t
  • abb0t
I will look through my notes from my kinetics class. If I find it, I'll post it.
anonymous
  • anonymous
ok thank u :)
anonymous
  • anonymous
@UnkleRhaukus
UnkleRhaukus
  • UnkleRhaukus
hmm , i haven't heard of the W- Lambert function before
anonymous
  • anonymous
do u have any idea @oldrin.bataku ??
anonymous
  • anonymous
W(x) is defined such that W(x) e^W(x) = x
anonymous
  • anonymous
yes.., i know.., i did read it on wikipedia. but I'm a little bit confused how to derive it (3rd equations) :)
anonymous
  • anonymous
I'm looking for some easy derivation of the above, step by step., :)
anonymous
  • anonymous
$$V_{max}t=([S_0]-[S](t))-K_M\ln\left(\frac{[S](t)}{[S_0]}\right)\\\ln\left(\frac{[S](t)}{[S_0]}\right)=\frac{[S_0]-[S](t)-V_{max}t}{K_M}\\\frac{[S](t)}{[S_0]}=\exp\left(\frac{[S_0]-[S](t)-V_{max}t}{K_M}\right)=\frac{e^\frac{{[S_0]-V_{max}t}}{K_M}}{\frac{e^{[S](t)}}{K_M}}$$ $$[S](t)e^{[S](t)}=\frac{S_0}{K_M}e^{\frac{[S_0]-V_{max}t}{K_m}}=\frac{S_0}{K_M}\exp\left(\frac{[S_0]-V_{max}t}{K_m}\right)$$ $$[S](t)=W\left(\frac{S_0}{K_M}\exp\left(\frac{[S_0]-V_{max}t}{K_m}\right)\right)$$
anonymous
  • anonymous
It's just algebra :-p
abb0t
  • abb0t
It is just algebra :) intense algebra.
anonymous
  • anonymous
i thank all of u guys :)
anonymous
  • anonymous
thank u so much @oldrin.bataku :)
anonymous
  • anonymous
$$V_{max}t=([S_0]-[S](t))-K_M\ln\left(\frac{[S](t)}{[S_0]}\right)\\\ln\left(\frac{[S](t)}{[S_0]}\right)=\frac{[S_0]-[S](t)-V_{max}t}{K_M}\\\frac{[S](t)}{[S_0]}=\exp\left(\frac{[S_0]-[S](t)-V_{max}t}{K_M}\right)=\frac{e^\frac{{[S_0]-V_{max}t}}{K_M}}{e^\frac{[S](t)}{K_M}}$$$$\frac{[S](t)}{K_M}e^\frac{[S](t)}{K_M}=\frac{[S_0]}{K_M}e^{\frac{[S_0]-V_{max}t}{K_M}}=\frac{[S_0]}{K_M}\exp\left(\frac{[S_0]-V_{max}t}{K_M}\right)$$$$\frac{[S](t)}{K_M}=W\left[\frac{[S_0]}{K_M}\exp\left(\frac{[S_0]-V_{max}t}{K_M}\right)\right]$$$$[S](t)=K_MW\left[\frac{[S_0]}{K_M}\exp\left(\frac{[S_0]-V_{max}t}{K_M}\right)\right]$$Sorry, I made a few really dumb errors the first time! http://en.wikipedia.org/wiki/Michaelis%E2%80%93Menten_kinetics#Determination_of_constants
anonymous
  • anonymous
ok.., no problem, thank u @oldrin.bataku ;)

Looking for something else?

Not the answer you are looking for? Search for more explanations.