what is the average rate of change for this exponential function for the interval from x = 1 to x = 3?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ over the interval $[a,b]$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1$, $b = 3$.

Step2: Estimate function values from the graph

From the graph, when $x = 1$, $y=f(1)\approx4$; when $x = 3$, $y=f(3)\approx15$.

Step3: Calculate the average rate of change

Substitute into the formula: $\frac{f(3)-f(1)}{3 - 1}=\frac{15 - 4}{2}=\frac{11}{2}=5.5$.

Answer:

$5.5$