# Exercise 3.1.4

Is $2^{n+1} = O(2^n)$? Is $2^{2n} = O(2^n)$?

Yes, because if we choose $2$ for both constants in the $O$-notation definition, we get an equality.

No, because $\nexists c: 2^n \cdot 2^n \leq c 2^n$.

Is $2^{n+1} = O(2^n)$? Is $2^{2n} = O(2^n)$?

Yes, because if we choose $2$ for both constants in the $O$-notation definition, we get an equality.

No, because $\nexists c: 2^n \cdot 2^n \leq c 2^n$.