Question

Graph info: A graph with a downward curved slope that starts at (-6, 5) goes downwards to create the f point of (-4, 0) going on until (-2, -3) continuing until the point of the curve at (0, -1) and now it begins to go back upwards, reaching through (2, -3) and going on to (4, 0) until it reaches the end point of (6, 5)

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

The quadratic: y(2) = −3 and y(6) = 5, so average rate = (5 − (−3)) / (6 − 2) = 8/4 = 2.

The exponential: y = (1/4)·2^x gives y(2) = 1 and y(6) = 16, so average rate = (16 − 1) / (6 − 2) = 15/4 = 3.75.

Comparison: 2 is 1.75 (7/4) less than 3.75, so the average rate of change of the quadratic is 1.75 less than the average rate of change of the exponential over [2,6].