Answer: The average rate of change is 6.
First, plug in each value of t into the function, v(t) to find there coordinate pairs.
v(2) = (2)^2 - (2) + 10
v(2) = 4 + 8
v(2) = 12
v(5) = (5)^2 - (5) + 10
v(5) = 25 + 5
v(5) = 30
You can write these values as coordinate pairs, like so: (2, 12) and (5, 30).
The formula for the average rate of change is [tex]A(x) = \frac{f(x)-(f(a)}{x-a} [/tex]. When you plug in the values from this particular case, the average rate of change formula becomes [tex]A(t) = \frac{30-12}{5-2} [/tex], or [tex]A(t)= \frac{18}{3} [/tex].
Looking at the equation, you can solve for the average rate of change between t = 2 and t = 5, which equals 6.
