Indicate whether the first function f$($n$)$ has a smaller, same or larger$$order$$of$$growth $($to within a constant multiple$)$ than g$($n$).$ Justify your answer$($prove that your answer is correct$).$

$$f$($n$)=2$ n$2+200$ n$$and$$g$($n$)=0\mathrm{.}001$ n$32$ n$2$