It still is exponential, but thankfully, the exponent seems to be dropping. In the US, and elsewhere in the world, too. If that drop was indeed only an artifact of limited testing, we would be f*cked - but I don’t believe the latter is the case, it might be a factor, but not exclusively.
I live in Germany and we did some, shall I say, half-assed social distancing, a lot stricter than “famous” Sweden but a lot less strict than France, Italy, or some places in the US AFAICT. For instance, you could still go for a walk, go to work (with the caveat that many workplaces were closed, mostly in retail, education and culture) or do grocery shopping. Assemblies of any kind, private or public, of more than 2 people at any time were prohibited though, and a vast majority of people stuck to that. Businesses switched to work-from-home on a huge scale to the point where for a few days, there were worries if our public Internet infrastructure could take it.
And still even if the lockdown was not what I would call draconic, it seems to have been pretty effective, with the number of new cases going down slowly, but steadily - not stalling but actually going down.
The number of daily deaths though, seems to be stable now - not diminishing, but not growing either, except for strong periodic variations when official bureaus close over the weekend, and many cases are reported at the start of the work week.
The big question seems to be now, can we push it down further with the measures we have in place? Or is that just an artifact of testing?