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

Explanation:

Step1: Recall multiplicative - rate formula

For an exponential function $y = ab^x$, the multiplicative rate of change $b$ is found by $\frac{y_{n + 1}}{y_n}$.

Step2: Calculate the ratio

Let's take the first two - values of $y$. When $x = 1,y_1=2$; when $x = 2,y_2=\frac{2}{5}$. Then $\frac{y_2}{y_1}=\frac{\frac{2}{5}}{2}=\frac{2}{5}\times\frac{1}{2}=\frac{1}{5}$. We can double - check with other consecutive values. When $x = 2,y_2=\frac{2}{5}$; when $x = 3,y_3=\frac{2}{25}$. Then $\frac{y_3}{y_2}=\frac{\frac{2}{25}}{\frac{2}{5}}=\frac{2}{25}\times\frac{5}{2}=\frac{1}{5}$.

Answer:

$\frac{1}{5}$