Question

compare the estimated average rate of change of the graphed quadratic function over the interval [2, 6] to the average rate of change of the exponential function y = 1/4 (2)^x

The average rate of change for the quadratic function for the interval [2, 6] is ____. The average rate of change for the exponential function is ____. The average rate of change of the quadratic function is ____ greater than/lesser than (choose) the average rate of change of the exponential function over the interval [2, 6]

Answer 1

I can compute the exponential one right away, but I need the quadratic’s values from the graph (or its equation) to get its average rate of change. Here’s how:

1. Exponential function y = (1/4)·2^x on [2,6]:
y(2) = (1/4)·2^2 = 1
y(6) = (1/4)·2^6 = 16
Average rate of change = (y(6) − y(2)) / (6 − 2) = (16 − 1) / 4 = 15/4 = 3.75

2. Quadratic function on [2,6]:
Average rate of change = (f(6) − f(2)) / 4.
I need f(2) and f(6) (or the quadratic’s equation) from the graph to compute this numeric value.

3. Comparison:
Once you give f(2) and f(6), I will compute the quadratic’s average rate of change and state whether it is greater than or less than 3.75.

If you post the graph values or the quadratic equation, I’ll fill in the blanks.