Question

Rank the following functions by order of growth (Highest running time to lowest running time):
1. $n \times 3^n$
2. $2^{\log(n)}$
3. $n^{2/3}$
4. $4^n$
5. $4^{\log(n)}$
Choose the correct answer from the options given below: 

• A. (E), (A), (D), (C), (B)
• B. (D), (A), (E), (B), (C)
• C. (D), (E), (A), (B), (C)
• D. (E), (D), (A), (B), (C)

Hint:

Exponential growth dominates polynomial growth, and logarithmic growth is the slowest.

Answer 1

The Correct Option is C

The growth order is evaluated as follows: - n × 3n: Exponential growth dominated by 3n. - 2lg n: Equivalent to n. - n2/3: Sub-linear polynomial growth. - 4n: Higher exponential growth compared to 3n. - 4lg n: Equivalent to n2, polynomial growth.