Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Discrete mathematics, probability and continuous mathematics / 2 / b / iv / Solution

The exponential function eventually grows faster than the fixed polynomial. A direct justification uses the ratio $r_n=4^n/n^4$:For all sufficiently large $n$, this ratio exceeds $2$, so $r_n$ grows without bound. The proposed Big O notation bound is therefore impossible: