Set 5: Exponential Functions

Choice A is correct. Choice A is the correct answer. Use properties of exponents. 1. Given: $e^{2 x} = 50$. 2. Rewrite: $e^{2 x} = (e^x)^2 = 50$. 3. Solve: $e^x = \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \approx 7.07$. Strategic Tip: $(a^m)^n = a^{mn}$, so $e^{2 x} = (e^x)^2$. Choice B is incorrect because $(e^x)^2 = 50$, not $e^x = 25$. Choice C is incorrect because this would give $e^{2 x} = 10000$. Choice D is incorrect because $e^x \neq e^{2 x}$.