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For which natural numbers n does the inequality 2ⁿ exceed n²?

1. n > 2
2. n > 3
3. n < 5
4. n ≥ 5

Correct answer: n ≥ 5

Solution

The inequality 2ⁿ exceeds n² for natural numbers n starting from 5, as for n = 5, 2⁵ = 32 and 5² = 25, and this trend continues for larger values of n due to the exponential growth of 2ⁿ compared to the polynomial growth of n².

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