Explain why the initial value of any function of the form

fx) = a (b') is equal to a.

the zero power of anything (except 0) is 1, so ab^0 = a·1 = a

Step-by-step explanation:

We assume you're concerned with the exponential function ...

f (x) = a (b^x)

The factor b^x will be b^0 when x=0. This is generally what we mean when we say "initial value."

The value of b^0 is always 1 (for any non-zero value of b). So the initial value of the function is ...

f (0) = a (b^0) = a (1) = a