$5)$

$5$a$)$ Calculate the final x$-$position of a $1$D mesh if the $\backslash (1^\{\backslash$text $\{$st $\}\}\backslash )$ grid spacing is $0\mathrm{.}05$ m and a geometric grid expansion rate of $\backslash (10\backslash \%\backslash )$ is used with $25$ grid spacings in total. Assume $\backslash ($ x $\backslash )$ starts at zero.

Ans: $4\mathrm{.}9$ m

$5$b$)$ What expansion ratio is required to make the final $\backslash ($ x $\backslash )-$coordinate $\backslash (=10\backslash ),$ using the above information?

Ans: $1\mathrm{.}146$