Wait, but if you plot the total number of cases with respect to time on a log-normal scale, you're still going to get a straight line, right? So why is plotting against time a bad idea?
You can't easily compare countries if you plot against time. China's outbreak was in February, USA's is now. As pointed out in the video (https://invidio.us/watch?v=54XLXg4fYsc), viruses don't care if it's March 29th or February 2nd. They are a "function" of the number of infected (and other parameters, but not time).
It depends on how you are modeling the data. In a logy plot, an exponential trend y=a * exp(b * x) appears linear, and is easiest to visualize/extrapolate. In a log-log plot, a power law y=a * x^b appears linear instead.
It depends partly on your assumptions, and how you are modeling it. An exponential curve assumes that all members of a population have equal contact with all other members of the population. A power law assumes that there is some social graph that maps into N dimensions, and that infections occur along an N-1 dimensional surface in that space. Either is a valid way to model the infection, and result in different preferred ways to plot the data.
