Explain why the initial value of any function of the form f(x) = a(bx) is equal to a.

Answer:

To find the initial value, we evaluate the function at x = 0. Substituting 0 for x in the equation f(x) = a(b^x) gives f(0) = a(b^0). Since any non-zero number raised to the zero power is 1, the expression simplifies to f(0) = a(1). Multiplying any number by 1 results in that number, so f(0) = a. Thus, the initial value is always a.