Those are total numbers- not per capita.
You don’t get exponential, do you? For ascertaining growth/doubling rates, the size of the region doesn’t matter, unless maybe you are talking about Luxembourg.
Where does one even begin? Since I'm a sucker for punishment, I'm going to try one more time. Here goes:
1. Exponential math involves a series progression ie 2-4-8-16-> Regardless of population, all epidemiology models utilize this function. Therefore, each initial series (by country) will appear very similar. Hence Matt's graph. Since CV has around a 7-14 day incubation before symptoms, individual country prevention/mitigation results won't appear until approx 3-4 weeks out. That is 1-2 weeks of dallying, denying, ignoring vs achtung out of the box, then everyone/most jump on the achtung wagon, but it will take another 7-14 days for any effects to appear.
2. "Cases" represents testing; not disease incidence. If you were clever, you could massage cases to form some kind of assumptions about statistical randomness. Once that had been performed, then you would have a valid sample size in which to project total outcomes. I'm assuming that's what Trump's team did. They of course are projecting for the total population - cases doesn't get you there by itself, but the Trump team would need something to represent a valid stat sample size (typically, around 1k).
3. Per capita doesn't mean anything in the short term for a couple of reasons. See #1 why - the series grows in similar patterns regardless of population size. Once controls/mitigation is in place, then per capita becomes an important measure of effectiveness. Second point, total population levels only represent saturation/threshold levels. That means a 5m country will grow at the same rate as a 500m country, all things being equal. The only difference is that the 5m country will reach saturation around 3m (60%), whereas the 500m country will be 300m.