Question $\backslash$#$2(4$ marks$)$: For $20$ keV x$-$rays, the LACs for different tissues are given in the table below $($units in $\backslash (\backslash$mathrm$\{$cm$\}^\{-1\}\backslash )).$ For each, find the thickness of that substance that would result in only $\backslash (10\backslash \%\backslash )$ of the initial x$-$ray beam passing through the tissue. Additionally, rank each material as they would appear on an x$-$ray from darkest to brightest.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|\}$

$\backslash$hline Material & $20$ keV & $50$ keV & $100$ keV $\backslash \backslash$

$\backslash$hline Air & $0\mathrm{.}001$ & $0\mathrm{.}0003$ & $0\mathrm{.}0002\backslash \backslash$

$\backslash$hline Bone & $5\mathrm{.}407$ & $0\mathrm{.}573$ & $0\mathrm{.}251\backslash \backslash$

$\backslash$hline Fat & $0\mathrm{.}517$ & $0\mathrm{.}193$ & $0\mathrm{.}154\backslash \backslash$

$\backslash$hline Muscle & $0\mathrm{.}872$ & $0\mathrm{.}24$ & $0\mathrm{.}180\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$