Good day everyone. In this appendix, particularly this part, the author approximated $1-aR$ with $e^h$ where $h=2.5$. Can anyone explain to me how did the author get this outcome? Variable $a$ is a parameter while $R$ is a real positive number.
I found myself with a similar expression looking like
$$Fe^{(-aR)}(1 + a -aR)$$
And I would like to attempt a similar "trick" to get rid of the $R$ in $-aR$ just like they did. Any help please?
The equation, as written in the appendix being $$M\Pi_t=K(1-a R_t)\,e^{-a R_t}$$ rewrite it as $$e^{-a R_t}=-\frac {M\Pi_t } {aK }\frac 1 { R_t-\frac 1a}$$and the solution is given in terms of the generalized Lambert function (have a look at equation $(4)$).