Set 5: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Calculate both values. 1. Calculate $e^\pi$: $e^{3.14159} \approx 23.14$. 2. Calculate $\pi^e$: $3.14159^{2.718} \approx 22.46$. 3. Comparison: $23.14> 22.46$, so $e^\pi > \pi^e$. Strategic Tip: This is a famous inequality: $e^\pi > \pi^e$. Choice B is incorrect because $\pi^e$ is slightly smaller. Choice C is incorrect because they are close but not equal. Choice D is incorrect because we can calculate both.