The problem arose from after reading the answer here:

How to adjust the parameters of Lotka-Volterra equations to fit the extremal values of each population

This is a composite function; $a= g(h(x_1/x_0)) $

where $g(z) = z - 1 - \ln z$, $h(z) = \frac{\ln z}{z-1} $ and $x_0 = 200000$ and $x_1 = 800000 $

The individual who provided the answer in the given link got $a = 3.2221 *10^4$

I get $0.23$ as the answer, which is obviously way off. I would really like to know how to solve this problem.

The individual in his answer (linked) implied the use of log to the base $e$ instead of simply using ln. This is what I was told anyways. Therefore, I used ln instead of log for the presentation of the problem here.

I am solving a similar problem and I need to understand how this is done.

  • $\begingroup$ Compute $y=h(x_1/x_0)$ and then $g(y)$. $\endgroup$ – Math Lover Dec 28 '17 at 19:35
  • $\begingroup$ @MathLover I did exactly that. so I compute h(4) right? and then g(h(4)) but my answer is always way off. $\endgroup$ – Selena Carlos Dec 28 '17 at 19:37
  • $\begingroup$ I solved the problem as follows:h(x1/x0) h(x_1/x_0)= ln (4)/3 =0.46 and then I solved for g (0.46) = 0.46 -1 - ln(0.46)=0.23 $\endgroup$ – Selena Carlos Dec 28 '17 at 19:44

Straight forward calculation, step by step. First, $\frac{x_1}{x_0}= \frac{800000}{200000}= 4$. Second, $h(4)= \frac{ln(4)}{4- 1}= \frac{ln(4)}{3}= 0.46210$. Finally, $g(0.46210)= 0.46210- 1- ln(0.46210)= 0.46210- 1+ 0.7720= 0.2341$.

Where did you get "32221"?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.