step 1
Find out the average rate of change function f over the interval [-1,2]
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
we have
a=-1
b=2
f(a)=f(-1)=-22
f(b)=f(2)=-1
substitute
[tex]\frac{-1-(-22)}{2-(-1)}=\frac{21}{3}=7[/tex]
step 2
Find out the average rate of change function g(x) over the interval [-1,2]
we have
a=-1
b=2
g(a)=g(-1)=-18(1/3)^-1+2=-52
g(b)=g(2)=-18(1/3)^2+2=0
substitute
[tex]\frac{0-(-52)}{2-(-1)}=\frac{52}{3}=17.3[/tex]
therefore
17>7
the answer is option A
