Problem: Solving Vmax equation with HP Prime
07-24-2018, 03:45 AM
Post: #1
 doun17 Junior Member Posts: 3 Joined: Jul 2018
Problem: Solving Vmax equation with HP Prime
Hi All

I recently got a HP Prime and am trying to solve a chemistry equation with little success. The formula appears below and calculating the result using traditional methods required two passes.

V = (Vmax * S) / (Km +S)

V and S are given and we need to calculate Vmax and Km

Manually we solve first for Vmax and then substitute that answer into the equation again to resolve for Km

I have tried countless ways of entering this in the Prime but I cannot get any valid results.
Can someone provide guidance on how I would go about solving this in the HP Prime

Thanks
07-24-2018, 04:57 PM
Post: #2
 xmehq Junior Member Posts: 24 Joined: Jan 2014
RE: Problem: Solving Vmax equation with HP Prime
At a glance, it appears that you are trying to solve for two unknowns (Vmax and Km) with a single equation. Is there a second equation that relates these two? Without a value for one of those, you (and your calculator) wouldn't be able to calculate the other unless there is another distinct equation to relate them.
07-24-2018, 05:22 PM
Post: #3
 Aries Member Posts: 139 Joined: Oct 2014
RE: Problem: Solving Vmax equation with HP Prime
(07-24-2018 03:45 AM)doun17 Wrote:  Hi All

I recently got a HP Prime and am trying to solve a chemistry equation with little success. The formula appears below and calculating the result using traditional methods required two passes.

V = (Vmax * S) / (Km +S)

V and S are given and we need to calculate Vmax and Km

Manually we solve first for Vmax and then substitute that answer into the equation again to resolve for Km

I have tried countless ways of entering this in the Prime but I cannot get any valid results.
Can someone provide guidance on how I would go about solving this in the HP Prime

Thanks

You have two unknowns but only a single equation.
You can't solve for two unknowns with only one equation (unless there are unusual side conditions).
Being the equation linear, you can solve for Vmax in terms of Km or Km in terms of Vmax.
Best,

Aries Post: #4
 roadrunner Member Posts: 276 Joined: Jun 2015
RE: Problem: Solving Vmax equation with HP Prime
Is that the Michaelis-Menten equation? If you have data for V and S plot 1/V vs 1/S in the statistic 2 variable app. If you use a linear fit the Y intercept is 1/Vmax, the slope is Km/Vmax and the x intercept is 1/Km.

edit: the x intercept is -1/Km

07-25-2018, 02:14 PM
Post: #5
 doun17 Junior Member Posts: 3 Joined: Jul 2018
RE: Problem: Solving Vmax equation with HP Prime
Hi

Thanks to everyones contribution to my problem, I was able to find the solution to the Michaelis-Menten equation. For those interested here is what I did.

In CAS mode

solve({48=v*0.2/k+0.2, 60=v*2/k+2},{v,k})

this gave the result of v=61.71 and k=5.71e-2

The correct solution!
07-25-2018, 02:15 PM
Post: #6
 doun17 Junior Member Posts: 3 Joined: Jul 2018
RE: Problem: Solving Vmax equation with HP Prime
(07-24-2018 06:16 PM)roadrunner Wrote:  Is that the Michaelis-Menten equation? If you have data for V and S plot 1/V vs 1/S in the statistic 2 variable app. If you use a linear fit the Y intercept is 1/Vmax, the slope is Km/Vmax and the x intercept is 1/Km.

edit: the x intercept is -1/Km