Question

Characterization of exponential functions. If for equal increments of a of the argument x, the values of the function f(x) change by the same ratio, that is f(x + a)/f(x) = b^(a) is constant (independent of x, but dependent on a), then the function is exponential with:

P = f(0) as initial value
a = f(1)/f(0) as base
f(x) = Pa^(x)

^ I do not understand how they came up with f(x +a)/f(x) = b^(a)