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

Explanation:

Step1: Recall rate - change formula

The multiplicative rate of change $r$ of an exponential function $y = a\cdot r^{x}$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $r=\frac{y_2}{y_1}$ when $x_2=x_1 + 1$.

Step2: Choose two consecutive points

Let's take the first two points $(x_1 = 1,y_1=6)$ and $(x_2 = 2,y_2 = 4)$.

Step3: Calculate the rate of change

$r=\frac{y_2}{y_1}=\frac{4}{6}=\frac{2}{3}$. We can double - check with other consecutive points. For example, if we take $(x_1 = 2,y_1 = 4)$ and $(x_2=3,y_2=\frac{8}{3})$, then $r=\frac{y_2}{y_1}=\frac{\frac{8}{3}}{4}=\frac{8}{3}\times\frac{1}{4}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$