To solve the expressions given:

Expression 1: $e^{-0.45}$

1. Calculate $e^{-0.45}$ using a calculator.
2. Round the answer to the nearest thousandth.

$e^{-0.45} \approx 0.637$

Expression 2: $150e^{0.3}$

1. Calculate $e^{0.3}$.
2. Multiply that result by 150.
3. Round the answer to the nearest thousandth.

$e^{0.3} \approx 1.350 \Rightarrow 150 \times 1.350 = 202.5$

Final Answers:

1. $e^{-0.45} \approx 0.637$
2. $150e^{0.3} \approx 202.5$

Would you like more details on these calculations or have further questions?

Here are five related questions for further practice:

1. How would you evaluate $e^{0.5}$ and round to the nearest thousandth?
2. What is the value of $200e^{-0.6}$ to the nearest thousandth?
3. How does changing the exponent from negative to positive affect the value of $e$?
4. What is the interpretation of $e$ in real-world exponential growth?
5. How do you handle exponential calculations without rounding intermediate steps?

Tip: Remember to avoid rounding until the final answer to ensure accuracy in exponential calculations.