Step-by-step explanation:
Step 1: Find the average rate of change
[tex]ARC = \frac{f(b)-f(a)}{b-a}[/tex]
Average Rate of Change is same as ARC
If you mean: [tex]f(x)=2x - \frac{1}{3}x+5[/tex]
[tex]ARC = \frac{f(8)-f(0)}{8-0}[/tex]
[tex]ARC=\frac{(2(8)-1/3(8)+5) - (2(0)-1/3(0)+5)}{8}[/tex]
[tex]ARC=\frac{(16-8/3+5)-(5)}{8}[/tex]
[tex]ARC=\frac{16-8/3}{8}[/tex]
[tex]ARC=\frac{40/3}{8}[/tex]
[tex]ARC=\frac{5}{3}[/tex]
If by the first way, the answer is: The average rate of change is 5/3
If you mean: [tex]f(x)=\frac{2x - 1}{3x+5}[/tex]
[tex]ARC=\frac{f(8)-f(0)}{8-0}[/tex]
[tex]ARC=\frac{\frac{2(8)-1}{3(8)+5}-\frac{2(0)-1}{3(0)+5} }{8}[/tex]
[tex]ARC=\frac{ \frac{15}{29} - \frac{-1}{5} }{8}[/tex]
[tex]ARC=\frac{\frac{ 104 }{ 145 } }{8}[/tex]
[tex]ARC=\frac{ 13 }{ 145 }[/tex]
If by the second way, the answer is: The average rate of change is 5/3
