To reframe the function in terms of the exponential function with base e, we need to leverage a key logarithmic identity, namely, that for any positive numbers a and b and any real number x, we have b^x = e^(ln(b)*x).
Applying this identity to the expression f(x) which is 2.5 * 6^x, we can rewrite 6^x as e^(ln(6)*x). Therefore, the function becomes f(x) = 2.5 * e^(ln(6)*x).
Now let's check each of the given options:
a) a = 2.5, r = 6: The equation becomes f(x) = 2.5 * e^(ln(6)*x), which is exactly our re-written function. So, this is the correct form.
b) a = 2.5, r = ln(6): This form will yield an equation f(x) = 2.5 * e^(ln(ln(6))*x), which is not equivalent to the original function. Hence, this is not the correct form.
c) a = 6, r = 2.5: The equation becomes f(x) = 6 * e^(ln(2.5)*x), which is also not equivalent to the original function. Hence, this form is not correct.
d) a = ln(6), r = 2.5: The equation becomes f(x) = ln(6) * e^(ln(2.5)*x), which is yet again not equivalent to the original function. Hence, this is not the correct form either.
Hence, we can clearly see that option a) with a = 2.5 and r = 6 is the correct choice. It is the only one that allows us to rewrite the function f(x) = 2.5 * 6^x in terms of the exponential function with base e.