To evaluate the expression $13,000 \cdot e^{0.03 \cdot 30}$, let's break it down step-by-step.

1. Evaluate the exponent: $0.03 \cdot 30 = 0.9$

2. Calculate $e^{0.9}$: Using the approximate value of $e^{0.9} \approx 2.4596$.

3. Multiply by 13,000: $13,000 \cdot 2.4596 = 31,974.8$

After rounding to two decimal places, the answer is:

$\boxed{31,974.80}$

Would you like more details, or do you have any questions?

Related Questions

1. What would happen if the exponent was 0.04 instead of 0.03?
2. How would you solve this if the base was 12,000 instead of 13,000?
3. Can you derive the general formula for $P \cdot e^{rt}$ where $r$ and $t$ are variables?
4. How does changing the exponent affect the growth rate in this type of equation?
5. What are some common applications of exponential functions in finance?

Tip: When dealing with exponential growth, small changes in the exponent can lead to significant differences in the final value.