Surface Expansion and Expected Remaining Time

On corresponding slide, the most important relationships in connection to the water lily growth are graphically represented:

Red Curve

The red curve shows the nonlinear increase in the surface area covered with water lilies as a percentage of the total pond surface:

• After more than 90 days, only 1% of the pond surface area is overgrown.
• After more than 125 days, 10% of the pond surface area is overgrown.
• After exactly 140 days, 25% of the pond surface area is overgrown.
• And 20 days later, the pond surface area is already completely overgrown.

Blue Curve

The blue curve represents the nonlinear decrease in the exposed pond surface area.

Light Blue Straight Lines

The pedestrian is not familiar with nonlinear functions. He would assume a linear decrease (light blue straight lines) in the exposed pond surface area. Each light blue line thus applies to a particular day of his visit to the pond. The straight line represents the length of time that the pedestrian would have assumed for the associated decrease in the exposed pond surface area on that visiting day.

By extending the light blue lines through the point of intersection with the timeline axis, the linearly thinking pedestrian would have estimated the time that apparently remained before the pond surface was completely covered.

For example, the line on the 140th day extends through the point of 75 % of exposed pond surface area. Thus, 20 days before the complete coverage of the pond, the line allows for a remaining time of 140÷25·75, or 420 days. The pedestrian calculates a date which lies 400 days (more than one year!) after the actual occurrence of the event.