When working with functions (of all types), the average rate of change is expressed using function notation:
[tex]\dfrac{f(b)-f(a)}{b-a}.[/tex]
For the interval from x=7 to x=8,
1. find f(7) and f(8):
- [tex]f(7)=729\cdot 3=2187;[/tex]
- [tex]f(8)=2187\cdot 3=6561;[/tex]
2. use given formula:
[tex]\dfrac{f(8)-f(7)}{8-7}=\dfrac{6561-2187}{8-7}=4374.[/tex]
Answer: the average rate of change for the interval from x=7 to x=8 is 4374.
