1. **Problem Statement:** Evaluate the function $h(x) = 1.5 e^x$ at the values $x = -1$, $x = \pi$, $x = 0.5$, and $x = \sqrt{2}$, rounding answers to two decimals. 2. **Formula:** The function is given by: $$h(x) = 1.5 e^x$$ where $e$ is Euler's number, approximately 2.71828. 3. **Calculations:** - For $x = -1$: $$h(-1) = 1.5 e^{-1} = 1.5 \times \frac{1}{e} = 1.5 \times \frac{1}{2.71828}$$ Intermediate step with cancellation: $$1.5 \times \cancel{\frac{1}{2.71828}}$$ Evaluated: $$h(-1) \approx 1.5 \times 0.36788 = 0.55$$ - For $x = \pi \approx 3.14159$: $$h(\pi) = 1.5 e^{3.14159}$$ Evaluated: $$h(\pi) \approx 1.5 \times 23.1407 = 34.71$$ - For $x = 0.5$: $$h(0.5) = 1.5 e^{0.5}$$ Evaluated: $$h(0.5) \approx 1.5 \times 1.64872 = 2.47$$ - For $x = \sqrt{2} \approx 1.41421$: $$h(\sqrt{2}) = 1.5 e^{1.41421}$$ Evaluated: $$h(\sqrt{2}) \approx 1.5 \times 4.11325 = 6.17$$ **Final answers:** $$h(-1) \approx 0.55, \quad h(\pi) \approx 34.71, \quad h(0.5) \approx 2.47, \quad h(\sqrt{2}) \approx 6.17$$