Help with a formula

01202015, 11:02 PM
Post: #1




Help with a formula
Trying to solve the following for "t"  but hitting bumps.
G(t) ...and WolframAlpha ignores me... solve for t Any hints or pointers? 

01202015, 11:10 PM
Post: #2




RE: Help with a formula
(01202015 11:02 PM)Geir Isene Wrote: Any hints or pointers? I don't see any algebraic solution (sum of exponentials, logs with added constants... I don't think you can solve this one). My suggestion is to give up. (use a numeric method to find roots for 't' if you need to solve for a specific value). Claudio 

01212015, 02:27 PM
Post: #3




RE: Help with a formula
(01202015 11:02 PM)Geir Isene Wrote: Trying to solve the following for "t"  but hitting bumps.Very interesting! Try to represent ln(e^###) in some other form. Even AFX2.0 tells "syntax error", not HP50G. HP50g, HP48gii, TI83 plus, FX2.0, CFX9850GB plus 

01212015, 08:09 PM
Post: #4




RE: Help with a formula
Hi,
Could you please explain further your problem ? Solving t of G(t): what does it refer to ? Dominique 

01212015, 08:13 PM
(This post was last modified: 01212015 08:15 PM by Geir Isene.)
Post: #5




RE: Help with a formula
(01212015 08:09 PM)Dominique Wrote: Hi, Here: http://isene.me/2015/01/10/hiddenrisko...urcingit/ (bottom equation) I specifically want to know what "t" is when G(t)=0 

01222015, 04:37 AM
Post: #6




RE: Help with a formula
(01212015 08:13 PM)Geir Isene Wrote: I specifically want to know what "t" is when G(t)=0 \(0 = \frac{T}{9}(\ln(e^\frac{8t}{T}+e^4)4)(1+D)  Dt\) \(Dt = \frac{T}{9}\ln(e^{\frac{8t}{T}4}+1)(1+D)\) \(t = \frac{T(1+D)}{9D}\ln(1+e^{\frac{8t}{T}4})\) This fixed point equation can be solved iteratively. With T=24 and D=0.5 I got t=0.1527. That's probably not what you want. However there's another fixed point at t~18.71 but unfortunately it's not attractive. In these situations we can use \(f^{1}(t)=t\) instead: \(\frac{9D}{T(1+D)}t=\ln(1+e^{\frac{8t}{T}4})\) \(e^{\frac{9D}{T(1+D)}t}1=e^{\frac{8t}{T}4}\) \(\ln(e^{\frac{9D}{T(1+D)}t}1)=\frac{8t}{T}4\) \(\frac{T}{8}(\ln(e^{\frac{9D}{T(1+D)}t}1)+4)=t\) After a few iterations we get t=18.713393. You can use this program for the HP42S: Code: 00 { 20 Byte Prgm } You just have to store \(T\) in register 00 and \(\frac{D}{1+D}\) in register 01, enter a guess and hit the [R/S] button a couple of times. Cheers Thomas 

01222015, 08:15 AM
Post: #7




RE: Help with a formula
(01222015 04:37 AM)Thomas Klemm Wrote:(01212015 08:13 PM)Geir Isene Wrote: I specifically want to know what "t" is when G(t)=0 Neat. Thanks Thomas. 

01242015, 05:00 PM
Post: #8




RE: Help with a formula
Adopted to the HP41 and with a better user interface. Start the program, enter the values for D and T and the program spits out "t" to the number of decimal places you have set with FIX:
Code:


02222015, 08:31 PM
Post: #9




RE: Help with a formula
An idea for a rough estimation  may not works for all D and T: With little algebra you can get: exp(m×t+b)+1=exp(a×t), where m=8/T, b=4 and a=9×D÷((1+D)×T)
For a rough estimation of t you can "forget" the +1 on the left side and the approximately solution for t is: t=b÷(am) = (4)÷(1÷81÷3) = 19.2 

02222015, 08:57 PM
Post: #10




RE: Help with a formula
Thanks :)


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