Which of the given options provides the increasing order of asymptotic…

Step-1: Compare growth rates

1. n log n

Grows slightly more than linear → smallest here.

2. n^1.5

Polynomial with power 1.5 → faster than n log n.

3. n^(log n)

This is super-polynomial but sub-exponential
because
n^(log n) = e^(log² n)

It grows faster than any n^k but slower than 2ⁿ.

4. 2ⁿ

Pure exponential → largest growth.

Final Increasing Order

f₃(n) = n log n
< f₂(n) = n^1.5
< f₄(n) = n^(log n)
< f₁(n) = 2ⁿ

Correct Option → A

A. f₃, f₂, f₄, f₁