Answer:
In this context:
[tex]\boxed{ARC=3}[/tex]
Explanation:
Hello! Remember you have to write complete questions in order to get good and exact answers. Here, I'll assume the exponential function is:
[tex]f(x)=2^x[/tex]
Every exponential function is a nonlinear function, and remember for any nonlinear function the slope changes at each point, so the average rate of change between any two points [tex](x_{1},f(x_{1}) \ and \ (x_{2},f(x_{2})[/tex] is the slope of the line through the two points:
[tex]ARC=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}} =\frac{Change \ in \ y}{Change \ in \ x}[/tex]
Here we set:
[tex]x_{1}=x=1 \\ \\ x_{2}=x=3 \\ \\ \\ So: \\ \\ f(x_{1})=2^1=2 \\ \\ f(x_{3})=2^3=8 \\ \\ \\ ARC=\frac{8-2}{3-1} \\ \\ \boxed{ARC=3}[/tex]
