Don't love the network graph illustrating the spread of a virus.
It's deceptive and is counter to the purpose of explaining exponential growth. If the people infected are represented by relatively uniform points on a plane, and infection is shown as an ever expanding circle, the growth is geometric, not exponential. I understand that the exponential growth could be captured by the acceleration of the radius, but that is not intuitive.
Actually it shows polynomial growth, not geometric growth. Polynomial growth is of the form t^n whereas geometric/exponential growth is of the form n^t. (The only real difference between geometric and exponential growth is that geometric connotes discrete growth steps; otherwise they are the same.)
In any case, I totally agree with your point. The virus graph is quite misleading because it shows a growing circle. The plot beside the graph doesn't even look like exponential growth!
Darn it, me too. I always thought geometric was a special case of polynomial where you only have a ax^2 term. I figured this was a reference to the fact that geometry is usually done in the plane, and linear increase corresponds to square increase in area.
I think I may have even pedantically "corrected" someone on this at some point. Awesome.
Comments
Don't love the network graph illustrating the spread of a virus.
It's deceptive and is counter to the purpose of explaining exponential growth. If the people infected are represented by relatively uniform points on a plane, and infection is shown as an ever expanding circle, the growth is geometric, not exponential. I understand that the exponential growth could be captured by the acceleration of the radius, but that is not intuitive.
Actually it shows polynomial growth, not geometric growth. Polynomial growth is of the form t^n whereas geometric/exponential growth is of the form n^t. (The only real difference between geometric and exponential growth is that geometric connotes discrete growth steps; otherwise they are the same.)
In any case, I totally agree with your point. The virus graph is quite misleading because it shows a growing circle. The plot beside the graph doesn't even look like exponential growth!
Yikes! I've been using "geometric growth" to mean "polynomial growth" my whole life.
Darn it, me too. I always thought geometric was a special case of polynomial where you only have a ax^2 term. I figured this was a reference to the fact that geometry is usually done in the plane, and linear increase corresponds to square increase in area.
I think I may have even pedantically "corrected" someone on this at some point. Awesome.