Linear relationships are among the easiest to use. You might not even need to pick up a pencil to know that if you’ve traveled at 50 miles per hour for 4 hours, then you’ve covered 200 miles.
But the world is not linear! Linearity is good to know about, and is perfect for its proper application, but not every relationship is a linear one.
This is why mathematics has other ways of constructing models of real phenomena. Two that show up in nature, and other places, are exponential and logarithmic models.
Exponential models can be as simple as a constant times a number raised to a variable power, and are a common choice for nonlinear models.
Logarithmic models are good for dealing with both the very large and the very small within a single model.
There are ten models for you to explore here, evenly divided among exponential and logarithmic models.
Each model can be controlled by using the sliders to set values for parameters and variables. Also numeric values may be typed into the accompanying text input boxes.
You can also drag certain graphical elements in the drawing area, like points, and horizontal and vertical lines.
The models can be used to answer the Explorations and Practice Questions.
Try all ten models. Feel free to manipulate any of the controls. See what you can learn beyond the Practice Questions. Have fun learning!