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 $y = a\cdot b^x$, the multiplicative rate of change $b$ can be found by dividing consecutive $y$ - values. Let's take $\frac{y_{n + 1}}{y_n}$.

Step2: Calculate the ratio

Take the second $y$ - value and divide it by the first $y$ - value. When $x = 1,y_1=6$ and when $x = 2,y_2 = 4$. Then $\frac{y_2}{y_1}=\frac{4}{6}=\frac{2}{3}$. We can double - check by taking the third $y$ - value and dividing it by the second $y$ - value. When $y_2 = 4$ and $y_3=\frac{8}{3}$, then $\frac{y_3}{y_2}=\frac{\frac{8}{3}}{4}=\frac{8}{3}\times\frac{1}{4}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$