The function you provided, \( f(x) = 100(1.25)^{x-1} \), is in the form of an exponential function. In general, exponential functions can be expressed as \( f(x) = a \cdot b^x \), where:
- \( a \) is a constant,
- \( b \) is the base of the exponential, and
- \( x \) is the exponent.
In this case, if you wish to identify the common ratio (similar to the concept of a common ratio in geometric sequences), you can look at the base of the exponent.
Here, \( b = 1.25 \). The term \( (1.25)^{x-1} \) can be rewritten using properties of exponents:
\[ f(x) = 100 \cdot (1.25)^x \cdot (1.25)^{-1} = \frac{100}{1.25} \cdot (1.25)^x \]
This indicates that as \( x \) increases by 1, \( f(x) \) is multiplied by 1.25. Thus, the common ratio of the function \( f(x) \) is:
\[ \text{Common Ratio} = 1.25 \]