Compare the estimated average rate of change of a quadratic function and an exponen...

The average rate of change for the quadratic function is $\frac{14 - (-2)}{6 - 2} = \frac{16}{4} = 4$. The average rate of change for the exponential function is $\frac{3}{4}(2)^6 - \frac{3}{4}(2)^2 = \frac{3}{4}(64) - \frac{3}{4}(4) = 48 - 3 = 45$. The difference is $45 - 4 = 41$. Re-evaluating the options, there might be a misunderstanding of the question or the provided options. Let's re-calculate based on the options provided. The quadratic function passes through (2, -2) and (6, 14). The average rate of change is $\frac{14 - (-2)}{6 - 2} = \frac{16}{4} = 4$. The exponential function is $y = \frac{3}{4}(2)^x$. At $x=2$, $y = \frac{3}{4}(2)^2 = \frac{3}{4}(4) = 3$. At $x=6$, $y = \frac{3}{4}(2)^6 = \frac{3}{4}(64) = 48$. The average rate of change for the exponential function is $\frac{48 - 3}{6 - 2} = \frac{45}{4} = 11.25$. The difference is $11.25 - 4 = 7.25$. The exponential function's average rate of change is greater.