the table represents an exponential function. what is the multiplicative rate of change of the…

Explanation:

Step1: Recall the formula for multiplicative rate of change

For an exponential function $y = ab^x$, the multiplicative rate of change is the common ratio $b$. To find it, divide a $y$-value by its previous $y$-value.

Step2: Calculate the ratio

Let's take the $y$-values for $x = 2$ and $x = 1$. When $x = 1,y=\frac{2}{1}=2$, when $x = 2,y = \frac{2}{5}$. The ratio is $\frac{\frac{2}{5}}{2}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}$. Let's double - check with another pair. When $x = 3,y=\frac{2}{25}$, and when $x = 2,y=\frac{2}{5}$. The ratio is $\frac{\frac{2}{25}}{\frac{2}{5}}=\frac{2}{25}\times\frac{5}{2}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$