Answer:
grows at a faster rate than the given quadratic function.
Explanation:
Given table:
First Differences in y-values:
Second Differences in y-values:
As the second differences are the same, the function is quadratic.
The coefficient of
is always half of the second difference.
Therefore, the quadratic function is:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
Therefore, the average rate of change for
over the interval
0 ≤ x ≤ 3 is:
An exponential function that grows at a faster rate than
over the interval 0 ≤ x ≤ 3 is
As 21 > 9,
grows at a faster rate than
over the interval 0 ≤ x ≤ 3.