The question is asking which of the given functions has a growth rate that belongs to the Big-O complexity class $O(2^n)$. Let's analyze the growth rates of the functions in the options:

• A: $n!$: The factorial function grows faster than exponential functions like $2^n$. Therefore, $n!$ is not $O(2^n)$.

• B: $3^n$: Since $3^n$ grows faster than $2^n$, $3^n$ is not $O(2^n)$. In fact, $2^n$ is $O(3^n)$.

• C: $n^2$: A polynomial function like $n^2$ grows much slower than an exponential function like $2^n$. Therefore, $n^2$ is $O(2^n)$.

• D: $n \log n + 4^n$: The term $4^n$ grows faster than $2^n$ since $4^n = (2^2)^n = 2^{2n}$. This implies that $4^n$ dominates the function and grows faster than $2^n$, so $n \log n + 4^n$ is not $O(2^n)$.

Correct answer: C: $n^2$

Would you like further clarification or have more questions on this topic?

Here are five related questions for further exploration:

1. What does Big-O notation represent in terms of algorithm complexity?
2. How does the growth rate of $n!$ compare to exponential functions like $2^n$?
3. Can you provide examples of other functions that are $O(2^n)$?
4. How does the function $n \log n$ compare in growth to $2^n$?
5. What are common mistakes when comparing growth rates of functions using Big-O notation?

Tip: When analyzing Big-O complexity, focus on the dominant term, especially for large $n$. This term dictates the growth rate of the function.