Solve for K

[andy_p]

Hi, this one stumped me (and it's been awhile since I tried these kind of jams).



How would I find K in this case? Thank you!

 

[Deleted member 4993]

Hi, this one stumped me (and it's been awhile since I tried these kind of jams).

View attachment 23468

How would I find K in this case? Thank you!

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[topsquark]

There is some kind of typo in the exponent of K in the numerator.

More generally, you can't solve for K. All you can do is solve it numerically.

-Dan

 

[andy_p]

Sure thing!

In simplest terms its a = b * ((K^z - 1)/(K-1))

or a/b = (K^z - 1)/(K-1)

now I know it's time to do a log, but I'm also not sure if I can get K^z-1 out somehow beforehand...

 

[andy_p]

There is some kind of typo in the exponent of K in the numerator.

More generally, you can't solve for K. All you can do is solve it numerically.

-Dan

Thanks Dan, I posted a little more of a clarification and where I'm stumped...

 

[Steven G]

Write it out as a polynomial in K. If z=1, then you have a linear equation which is easy to solve, if solvable. If z=2, then you can could solve using the quadratic formula and if z=3 you could always solve using the cubic formula. Hopefully, especially if z>3 or a non integer, you can see an answer or two. However in general, tops quark is correct in saying that all you can do is solve it numerically or with software.

 

[Steven G]

Thanks Dan, I posted a little more of a clarification and where I'm stumped...

This does not help. Dan's response is still valid. Logs will not help at all.

 

[andy_p]

Thanks everyone, yup just ended up doing this as a function...

function findK (Ut, U0, t, Ct){
var K = .0001
while ((Ut / (U0 * ((K**(t/Ct))-1)/(K-1))) > 1.001) {
K = K + .0001
}
return K
}