# Linear vs Exponential Rate of Change

- Author:
- StudyForge Interactives

Here we will investigate and compare the rate at which Linear (Green) and Exponential (Blue) 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 Linear 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)
• Does it appear that the exponential curve will ever intersect the line?
• Change the zoom until exponential function grows faster and intersects the linear graph. Estimate this intersection point.
Part II
• Move Linear Slider to the middle (to increase the slope)
• Change the zoom slider until the exponential intersects the linear graph. What is the approximate intersection point?
Part III
• Move Linear Slider all the way to the right (increasing slope to the maximum) and the Exponential slider all the way to the left (decreasing the slope).
• Does it appear the exponential curve could ever intersect the line now?
• Change the zoom slider to test your hypothesis.
• What conclusion can we make regarding how fast lines grow compared to exponential curves?