Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 18, is less than or equal to, x, is less than or equal to, 3618≤x≤36.
To find the average rate of change of a function over an interval, we use the formula:
Average Rate of Change = (f(b) - f(a))/(b - a)
where f(b) and f(a) represent the values of the function at the endpoints of the interval, and b and a represent the x-values of the endpoints.
In this case, the interval is from 18 ≤ x ≤ 36. So, a = 18 and b = 36.
Using the table, we can find the corresponding values of the function at these x-values.
f(a) = 72 and f(b) = 180.
Now, we can substitute these values into the formula to find the average rate of change:
Average Rate of Change = (f(b) - f(a))/(b - a)
= (180 - 72)/(36 - 18)
= 108/18
= 6
So, the average rate of change of the function over the interval 18 ≤ x ≤ 36 is 6.