Problem $1.$ Order the following functions by asymptotic order of growth $($lowest to highest$)$

$($a$)10000+200n+90n^2+55n^{2}logn+1\mathrm{.}1n^3$

$($b$)5nlogn+4n$

$($c$)5n^3$

$($d$)10n+2$

$($e$)n$

$($f$){400}^{3}logn$