Question 1046357
<font face="Times New Roman" size="+2">


You need to set the two functions equal to each other and then solve for *[tex \Large n].  The problem with that idea is that you end up with:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ n\ =\ \frac{W_m\left(10240\ln(2)\right)\ -\ 8\ln(2)}{\ln(2)}]


Where *[tex \Large W_m\left(10240\ln(2)\right)] is a Lambert W-Function that requires a mighty ugly Taylor Series expansion to evaluate.


On the other hand, if you graph the two functions, it looks like they intersect at the point *[tex \Large (2,10)].


 *[illustration economicefficiency_(2).jpg]


And lo and behold:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8\ +\ 2\ =\ 10]


And


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 40\left(\frac{1}{2}\right)^2\ =\ 40\left(\frac{1}{4}\right)\ =\ 10]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>