To evaluate the function $f(x) = 2.3e^{2x - 0.1}$ at $x = 2$:

Step 1: Substitute $x = 2$ into the function:

$f(2) = 2.3e^{2(2) - 0.1}$

Step 2: Simplify the exponent:

$2(2) - 0.1 = 4 - 0.1 = 3.9$ $f(2) = 2.3e^{3.9}$

Step 3: Compute $e^{3.9}$:

Using a calculator or computational tool: $e^{3.9} \approx 49.402449$

Step 4: Multiply by 2.3:

$f(2) = 2.3 \times 49.402449 \approx 113.6256$

Final Answer:

$f(2) \approx 113.6256$

Let me know if you would like more details or have any questions! Here are some related queries for further exploration:

1. What is the derivative of $f(x) = 2.3e^{2x - 0.1}$?
2. How does the value of $f(x)$ change as $x \to \infty$?
3. Evaluate $f(x)$ for other values of $x$, such as $x = 1$ or $x = 0$.
4. Can we rewrite $f(x)$ in terms of logarithmic functions?
5. How is $f(x)$ affected if the constant $2.3$ changes to another value?

Tip: When working with exponential functions, ensure your calculator is in the correct mode to handle $e$-based calculations.