The table describes the growth of a function of the form \( f(x) = a \cdot b^x \), which is an exponential function. The derivation shows that the ratio of the function values over equal intervals (specifically \( \Delta x \)) is constant and equal to the growth factor \( b^{\Delta x} \).
This indicates that as \( x \) increases by equal increments (specifically \( \Delta x \)), the function values grow by a constant multiplicative factor.
Therefore, the correct option is:
Option #4: Over equal intervals, exponential functions grow by equal factors.