What does exponential growth look like?

Hopefully at this point in your career as a biology student, you have seen a graph of exponential growth. Rather than show you a picture right away, use your mouse to draw an exponential curve (specifically, starting at 1 and doubling at each timestep) on the graph below.

Then click on the "graph" button to see how close you got. (You can also use the slider to set different initial population sizes and try to predict the curve).

If you take the log of an exponential growth curve, the graph "unbends" itself and turns into a straight line. This kind of graph is called "log-transformed."

What happens is a series of numbers that are evenly spaced on a linear scale get spaced differently on a log scale: specifically, on a log scale, the largest numbers get squished together, while the smallest numbers get stretched apart.

In the applet below, you can log-transform the graph of exponential growth, and then transform it "back" to a normal graph. Watch also how the evenly spaced points on the y-axis get stretched and squished.