The average rate of change of a function [tex]f(x)[/tex] in the interval [tex][a,b][/tex] is defined as
[tex] A(a,b,f) = \dfrac{f(b)-f(a)}{b-a}[/tex]
So, in your case, we have
[tex]A(9,11,3^x-9) = \dfrac{(3^{11}-9)-(3^9-9)}{11-9} = \dfrac{3^{11}-3^9-9+9}{2} = \dfrac{157464}{2}=78732[/tex]
