Comparing average rates of change for an exponential and a quadratic function.

Calculate the average rate of change for $y=4^x$ and $y=4x^2$ over $[0, 1.1]$. For $y=4^x$, the average rate of change is $\frac{4^{1.1}-4^0}{1.1-0} \approx \frac{4.525-1}{1.1} \approx 3.205$. For $y=4x^2$, the average rate of change is $\frac{4(1.1)^2-4(0)^2}{1.1-0} = \frac{4(1.21)-0}{1.1} = \frac{4.84}{1.1} = 4.4$. The quadratic function has a greater average rate of change.