We are given the function:

$f(x) = 2 \times 3^x - 3.15^x$

where $x$ can only take whole numbers between 0 and 15. Our task is to determine for which value of $x$ the function reaches its maximum value, and to compute that maximum.

To solve this, we can:

1. Compute the value of the function for each $x$ from 0 to 15.
2. Identify the $x$ that gives the maximum value of $f(x)$.

Let's calculate the values for $f(x)$.The function $f(x) = 2 \times 3^x - 3.15^x$ reaches its maximum value when $x = 13$. The maximum value of the function is approximately $182312.20$.

Would you like more details or explanations on this result?

Here are some related questions to explore further:

1. What happens to the function as $x$ approaches 15 or higher?
2. How does changing the base of the exponent affect the behavior of $f(x)$?
3. Can the function have other local maxima within a different range of $x$?
4. How would the function behave if the coefficients were altered (e.g., instead of 2 and 3.15)?
5. What physical scenario could this function represent?

Tip: When dealing with exponential functions, slight changes in the base can drastically affect the function's growth.