In the exponential function \( f(x) = 100(1.25)^{x-1} \), the common ratio is the factor by which the function value changes for each unit increase in \( x \).
Here, the base of the exponent is \( 1.25 \). This means that for each increase of 1 in \( x \), the function value is multiplied by \( 1.25 \).
Therefore, the common ratio in the equation is \( 1.25 \).