Question

Common ratio for f (x) = 100(1.25)^x-1

Answer 1

The function you provided, \( f(x) = 100(1.25)^{x-1} \), is an example of an exponential function. In this context, the common ratio refers to the factor by which the function's value multiplies as \( x \) increases by 1.

In the general form of the function \( f(x) = a \cdot r^{(x - k)} \), where:
- \( a \) is a constant (the initial value),
- \( r \) is the common ratio, and
- \( k \) is a constant offset in the exponent.

Here, your function can be rewritten as:

\[
f(x) = 100(1.25)^{x - 1}
\]

In this case, the common ratio \( r \) is \( 1.25 \). This means that for each increment of 1 in \( x \), the function value \( f(x) \) is multiplied by \( 1.25 \).

To summarize, the common ratio of the function \( f(x) = 100(1.25)^{x - 1} \) is:

\[
\text{Common Ratio} = 1.25
\]