In theory, the exponential growth rate of the virus doesn't depend on the population size. It more strongly depends on the population structure - i.e. the average number of social contacts made in a day.
If you start with a hypothesis that this virus is in wide global circulation already, all this testing is doing is confirming “yup, people have the virus!”.
Only way to prove or disprove the hypothesis that the virus is widespread is large scale testing of a truly random subset of the entire population. Last I checked that isn’t happening anywhere in the United States and possibly elsewhere.
Why is proving that hypothesis important? Because if true it means the severity of this virus is dramatically less than our limited data suggests. If true, most of the rather draconian measures we are taking are pointless.
If false, god help us all I guess...
As does (albeit in a weaker form) the testing of the full population of Vò.
As does the testing in at least a few European countries, where the growth rate of tests outpaces that of confirmed infections. And/or where the number of tests administered vastly exceeds the number of confirmed infections.
Sure, once we have anti-body tests widely available, the data will become better.