The total amount after 10 years, $A(10)$, is approximately $2983.65.

Would you like more details or have any questions?

Here are 5 related questions you might want to explore:

1. What is the value of $A(t)$ after 15 years?
2. How does the formula change for different interest rates?
3. What would the amount be if the initial investment was $3,000 instead?
4. How do we calculate the amount for discrete compounding instead of continuous compounding?
5. What is the time $t$ required for the investment to double?

Tip: Continuous compounding uses the formula $A = P e^{rt}$, where $P$ is the principal, $r$ is the rate, and $t$ is the time.