The image contains three mathematical functions that need to be evaluated at specific values. Let's solve each one step by step.

a. $f(x) = 1.4e^{3x} - 0.8$, and we need to find $f(4)$:

$f(4) = 1.4e^{3(4)} - 0.8$

b. $g(x) = 2.1 \cdot 4^{-x+3} + 1.4$, and we need to find $g(-2)$:

$g(-2) = 2.1 \cdot 4^{-(-2)+3} + 1.4 = 2.1 \cdot 4^{2+3} + 1.4$

c. $h(x) = -5e^{x-3}$, and we need to find $h(-3)$:

$h(-3) = -5e^{-3-3} = -5e^{-6}$

I'll calculate the values now.Here are the evaluated values for the given functions:

a. $f(4) \approx 227855.9080$

b. $g(-2) = 2151.8000$

c. $h(-3) \approx -0.0124$

Would you like more details on any step, or have any questions?

Here are some related questions to explore further:

1. What is the impact of exponentials on the growth of functions like $f(x)$ and $g(x)$?
2. How do logarithmic transformations affect inverse problems in exponential functions?
3. What is the role of the base in exponential functions like $g(x)$?
4. How does negative exponentiation affect the function $h(x)$?
5. How are exponential functions used in real-world applications, such as population growth or decay?

Tip: When dealing with exponential expressions, rounding errors can grow quickly, so keep as many decimals as possible until the final result.