Answer
n=23
Work Step by Step
At n=1
$100\times n^{2}$ = 100
$0.01\times 2^{n}$ = 0.02
At n=2
$100\times n^{2}$ = 400
$0.01\times 2^{n}$ = 0.04
At n=3
$100\times n^{2}$ = 900
$0.01\times 2^{n}$ = 0.08
....
At n=22
$100\times n^{2}$ = 48400
$0.01\times 2^{n}$ = 41943
At n=23
$100\times n^{2}$ = 52900
$0.01\times 2^{n}$ = 83886
So at n=23, 100$n^{2}$ becomes better.
