Answer
See the explanation
Work Step by Step
To determine when the algorithm with time complexity
$n^4$ is more efficient than the one with time complexity
$4n$, we need to find the values of $n$ for which:
$n^4<4n$
We solve for $n$:
$n^3<4$
$n<\sqrt[3]4\approx 1.587$
The algorithm with time complexity $n^4$ is more efficient than the one with time complexity
$n^4$ only when $n<1.587$.
Since $n$ must be a positive integer, the only value that satisfies this is:
$n=1$
Therefore for very small input sizes (specifically
$n=1$ the $n^4$ algorithm may perform fewer operations than the $4n$ algorithm.
But for any larger input, the exponential growth of $n^4$ quickly overtakes the linear growth of $4n$.
