To find the average rate of change, use the following formula:
[tex] \frac{f(b) - f(a)}{b-a} [/tex]
a and b represent the values of the interval:
[tex]a = 0, b = 8[/tex]
Simplify the original equation by combining like terms:
[tex]2x - 13x = -11x[/tex]
[tex]f(x) = -11x + 5[/tex]
Plug the interval values into the f(x) equation:
[tex]f(0) = -11(0) + 5 = 0 + 5 = 5[/tex]
[tex]f(8) = -11(8) + 5 = -88 + 5 = -83[/tex]
Plug in these values into the average rate of change formula:
[tex] \frac{-83 - 5}{8 - 0} = \frac{-88}{8} = -11[/tex]
The average rate of change over this interval is -11.
