the average rate of f(x) from x=a to x=b is the slope from (a,f(a)) to (b,f(b)) or [tex]\frac{f(b)-f(a)}{b-a}[/tex]
for this problem
[tex]f(x)=2(3)^x[/tex]
from x=2 to x=4
find f(2) and f(4)
[tex]f(2)=2(3)^2=2(9)=18[/tex]
[tex]f(4)=2(3)^4=2(81)=162[/tex]
so average rate of change from x=2 to x=4 is
[tex]\frac{f(4)-f(2)}{4-2}=\frac{162-18}{4-2}=\frac{144}{2}=72[/tex]
the average rate of change from x=2 to x=4 is 72
