Quadratic vs Exponential Rate of Change

Here we will investigate and compare the rate at which Quadratic (Red) and Exponential (Green) Functions change. On the graph we have three sliders that are used to manipulate different parts of the graph. Follow the instructions below and answer the corresponding questions.
Part I • Start with: o Quadratic Slider all the way to the left o Exponential Slider all the way to the right o Zoom Slider all the way down (zoomed in) • Which function is growing faster here? Part II • Move Quadratic Slider all the way to the right. • Which curve is growing faster now? • Move the zoom slider until the Exponential curve intersects the Quadratic curve and estimate this intersection point. • Which curve is growing faster now? Part III • Move Exponential Slider move all the way to the left. • Which curve is growing faster now? • Based on what we have learned, what do you think will happen when we zoom out even further? Test your hypothesis. • What conclusion can we make concerning the rate of change in quadratics compared to exponential functions?