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The given function is:

\[
f(x) = 250 e^{0.05x}
\]

You are asked to evaluate this at \(x = 20\) and round the result to three decimal places.

Let's calculate \(f(20)\):

\[
f(20) = 250 e^{0.05 \times 20}
\]

First, calculate \(0.05 \times 20 = 1\), so:

\[
f(20) = 250 e^1
\]

Since \(e \approx 2.71828\):

\[
f(20) = 250 \times 2.71828 \approx 679.57
\]

Thus, \(f(20) \approx 679.570\) when rounded to three decimal places.

Let me know if you want more details or have any other questions!

Here are 5 follow-up questions to consider:
1. How does the exponential function behave for other values of \(x\)?
2. What is the significance of the constant \(e\) in exponential growth?
3. How would the graph of this function look for values of \(x\) between 0 and 20?
4. What happens to \(f(x)\) as \(x\) approaches infinity?
5. How would changing the coefficient \(0.05\) affect the growth of the function?

**Tip:** When dealing with exponential functions, the base \(e\) represents natural growth processes and has applications in fields like biology, economics, and physics!

Evaluate f(x) = 250e^{0.05x} at x = 20, round to three decimal places.

Learn how to evaluate the natural exponential function f(x) = 250e^{0.05x} at x = 20. This detailed solution involves calculating the value of f(20) and rounding to three decimal places. Suitable for students in Grades 10-12.

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