2.7 Growth, exponential and otherwise
Many people who use the phrase ‘‘exponential growth’’ use it incorrectly, somehow thinking it only means ‘‘very fast.’’ Exponential growth involves, well, exponents. Here’s a plot showing four kinds of growth: exponential, quadratic, linear, and logarithmic.
I’ve drawn them so they all intersect at a point but afterwards diverge. After the convergence, the logarithmic plot (dot dashed) grows slowly, the linear plot (dashed) continues as it did, the quadratic plot (dotted) continues upward as a parabola, and the exponential one shoots up rapidly.
Take a look at the change in the vertical axis, the one I’ve labeled resources with respect to the horizontal axis, labeled problem size. As the size of the problem increases, how fast does the amount of resources needed increase? Here a resource might be the time required for the algorithm...
