Question

What is the average rate of change for the function f(x)=3^x-9 9 less than or equal to x less than or equal to 11

Answer 1

The average rate of change of a function $f(x)$ in the interval $[a,b]$ is defined as

$A(a,b,f) = \dfrac{f(b)-f(a)}{b-a}$

So, in your case, we have

$A(9,11,3^x-9) = \dfrac{(3^{11}-9)-(3^9-9)}{11-9} = \dfrac{3^{11}-3^9-9+9}{2} = \dfrac{157464}{2}=78732$