what is the multiplicative rate of change for the exponential function graphed to the left?

Explanation:

Step1: Recall multiplicative - rate formula

For an exponential function $y = ab^x$, the multiplicative rate of change is $b$. Given two 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 points $(0,2)$ and $(1,6)$. Here $x_2=1$, $x_1 = 0$, $y_2 = 6$, $y_1=2$.

Step3: Calculate the multiplicative rate of change

Using the formula $b=\frac{y_2}{y_1}$, we substitute the values: $b=\frac{6}{2}=3$.

Answer:

3