The average reader can probably easily imagine y=2 to y=2x to y=X^2 relationship, but its becomes harder when the rates change. Visualizing y=N to y=Nx to y=x^

The average reader can probably easily imagine y=2 to y=2x to y=X^2 relationship, but its becomes harder when the rates change. Visualizing y=N to y=Nx to y=x^N where N is any given number is fairly hard to see accurately in my head since it adds a new dimension (time) to the visualization. Giving a slider where N can be visualized over time shows how changes in N accelerates y=x^N away y=Nx. These compound complexities better seen in interactive widget as the average mind is not well equipped to visualize them.