Something I never thought about: when simple exponential growth is explained in DE, examples usually include things like interest rates etc
and the solution usually takes the following form: $y=Ce^{rt}$ where r is the interest rate.

However, the coronavirus infection growth is typically represented as $y=r^t$ which is brilliant.
It is simple and concise since r represents the doubling rate in days! I wonder why this notation isn't ALWAYS used.

If you think about it, there is a simple relationship between them as r2=e^r1 and r1 = ln(r2). That's it!
And of course when you need to solve problems like, what should be the interest rate for your account to double in x years, it is a little
more convenient to calculate since it is just $\dfrac{\ln{2}}{x}$. And a related problem, given x find r, doesn't change much
since the starting point for both is $\ln{2}=rx$

Whereas the second form $y=r^t$ requires calculating an awkward radical like
$\sqrt[x]{2}$. For example if the infection doubling rate in NY is 10 days, the rate of infection is
$\sqrt[10]{2}$ which is not easy to google so I have to pull out my old TI-83 calculator to get 1.071.
But admittingly, if I need to do the opposite and I know the the infectio rate is 1.2, then the doubling rate is $\dfrac{\ln{2}}{\ln{r}}$
which is easy to calculate (3.8 days).

So which is right which is wrong? Which is good which is bad? I know it is pretty advanced stuff but I think I am good at it now.
(If you noticed any mistakes please let me know!)