To determine the multiplicative rate of change for an exponential function given the table of values, we'll examine the relationship between consecutive [tex]\( y \)[/tex]-values.
[tex]\[
\begin{tabular}{|c|c|}
\hline
x & y \\
\hline
1 & 0.25 \\
\hline
2 & 0.125 \\
\hline
3 & 0.0625 \\
\hline
4 & 0.03125 \\
\hline
\end{tabular}
\][/tex]
For an exponential function, the multiplicative rate of change is the ratio of any [tex]\( y \)[/tex]-value to the previous [tex]\( y \)[/tex]-value.
Let's calculate this ratio using the first two pairs of [tex]\( y \)[/tex]-values. Specifically, we will consider:
[tex]\[
\text{Rate of change} = \frac{\text{y-value at } x=2}{\text{y-value at } x=1} = \frac{0.125}{0.25}
\][/tex]
Dividing these values:
[tex]\[
\frac{0.125}{0.25} = 0.5
\][/tex]
Therefore, the multiplicative rate of change of the function is [tex]\( 0.5 \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{0.5}
\][/tex]
