I'm not sure how it's exponential, if you look at the graph for the current # of cases [0], then you can see it's more or less flat (and the new case %-age has been around 2-3%), between deaths and (most) people recovering, the number of active cases must at least flat and most likely getting smaller?

[0] https://en.wikipedia.org/wiki/COVID-19_pandemic_in_Massachus...