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 $y = a\cdot b^x$, the multiplicative rate of change is $b$. Given two - consecutive points $(x_1,y_1)$ and $(x_2,y_2)$ on the exponential function, $b=\frac{y_2}{y_1}$ when $x_2=x_1 + 1$.

Step2: Select two consecutive points

Let's take the first two points $(x_1 = 1,y_1=\frac{3}{2})$ and $(x_2 = 2,y_2=\frac{9}{8})$.

Step3: Calculate the multiplicative rate of change

$b=\frac{y_2}{y_1}=\frac{\frac{9}{8}}{\frac{3}{2}}=\frac{9}{8}\times\frac{2}{3}=\frac{3}{4}$

Answer:

$\frac{3}{4}$