The numbers are growing exponentially until they don't. You can argue that they would have, had extreme measures not been put in place, and there are reasonable arguments for that. But you have to keep track of the fact that it is an argument you're making and not an observation directly from the data. Otherwise you won't update properly on new information.
For example, one thing I've seen people worry about is that there could be huge numbers of undetected infections; one guy quoted me 1.5 million for the US's 40k known cases. This would be wonderful news if true - death rates and hospitalization rates are 37 times smaller than believed, and the theoretical peak is nearer than we'd thought? But I've universally seen people present these scenarios as bad news, because they've internalized "numbers going to grow exponentially" as an observed fact rather than a contingent conclusion.
In every country where we have seen case load sigmoid out, there have been heavy mitigation and suppression efforts put in place that preceded it by several weeks. Thus far, many European countries and the US have only just started to get serious about this. Therefore I am fairly confident that we will be in the exponential growth phase for a while longer.
For example, one thing I've seen people worry about is that there could be huge numbers of undetected infections; one guy quoted me 1.5 million for the US's 40k known cases. This would be wonderful news if true - death rates and hospitalization rates are 37 times smaller than believed, and the theoretical peak is nearer than we'd thought? But I've universally seen people present these scenarios as bad news, because they've internalized "numbers going to grow exponentially" as an observed fact rather than a contingent conclusion.