Exponentially; powerful

What this exponential inequality proof question tests

This is an easy puzzle that asks you to prove a fundamental inequality comparing exponential and polynomial growth. It's the kind of question used to assess whether a candidate can construct a clear, logical argument and choose an appropriate proof technique.

The core skill being tested is recognizing when an inequality holds for all integers above a threshold, and selecting the right method to establish it. Candidates often consider induction, direct calculation, or algebraic manipulation. The question rewards clean reasoning and the ability to verify a base case before generalizing.

• Mathematical induction
• Base case verification
• Growth rates and asymptotic behaviour
• Algebraic inequality manipulation