https://file.aiquickdraw.com/mathbot/file/1730675423755sozf6lxf.jpg

To solve this problem, we need to evaluate the function \( f(x) = 300e^{(0.02x)} \) at \( x = 48 \), and then round the answer to three decimal places.

### Steps to solve:

1. **Substitute \( x = 48 \)**:
   \[
   f(48) = 300e^{(0.02 \times 48)}
   \]

2. **Calculate the exponent**:
   \[
   0.02 \times 48 = 0.96
   \]

   So, we now have:
   \[
   f(48) = 300e^{0.96}
   \]

3. **Evaluate \( e^{0.96} \)** (using the value of \( e \approx 2.718 \)):
   \[
   e^{0.96} \approx 2.6117
   \]

4. **Multiply by 300**:
   \[
   f(48) \approx 300 \times 2.6117 = 783.51
   \]

5. **Round to three decimal places**:
   \[
   f(48) \approx 783.510
   \]

### Final Answer:
\[
f(48) = 783.510
\]

Would you like a more detailed explanation or have any questions?

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Here are some related questions to deepen understanding:

1. What would \( f(x) \) equal if \( x = 50 \) instead of 48?
2. How does changing the coefficient 300 affect the function's value?
3. What is the impact of changing the exponent base \( e \) to a different value?
4. How can we interpret the significance of \( e^{0.02x} \) in real-world applications?
5. What happens to \( f(x) \) as \( x \) approaches infinity?

**Tip:** Always double-check exponent calculations, as small errors in exponent values can significantly impact the result.

Evaluate the function \( f(x) = 300e^{(0.02x)} \) at \( x = 48 \), rounding the result to three decimal places.

Learn how to evaluate the exponential function f(x) = 300e^(0.02x) at x = 48, with step-by-step instructions and rounding to three decimal places. This problem demonstrates key concepts in exponential functions and is suitable for high school students in Grades 9-12.

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