import numpy as np

Define the function h(x) = e^(-3x)

def h(x): return np.exp(-3 * x)

Calculate h(x) for the given values

values = { "h(1/3)": h(1/3), "h(1.5)": h(1.5), "h(-1)": h(-1), "h(-π)": h(-np.pi) }

Round the results to three decimal places

rounded_values = {key: round(val, 3) for key, val in values.items()} rounded_values{'h(1/3)': 0.368, 'h(1.5)': 0.011, 'h(-1)': 20.086, 'h(-π)': 12391.648}{'h(1/3)': 0.368, 'h(1.5)': 0.011, 'h(-1)': 20.086, 'h(-π)': 12391.648}successHere are the rounded values for the function $h(x) = e^{-3x}$:

1. $h\left(\frac{1}{3}\right) = 0.368$
2. $h(1.5) = 0.011$
3. $h(-1) = 20.086$
4. $h(-\pi) = 12391.648$

Do you want further explanation or details on how these values were computed?

Here are 5 related questions to expand your understanding:

1. How does the value of $e^{-3x}$ change as $x$ becomes more positive or negative?
2. What is the general effect of a negative exponent on the behavior of exponential functions?
3. How does the base $e$ influence the properties of $e^{-3x}$ compared to other exponential bases?
4. How would the graph of $h(x) = e^{-3x}$ look for $x \in [-\pi, 2]$?
5. Can the function $h(x)$ ever reach a value of 0? Why or why not?

Tip: When rounding intermediate results for exponential functions, always ensure the precision aligns with the context of the problem!