It certainly looks exponential until mitigation/suppression measures are put in place or you reach herd immunity. Guess which of the two will result in more deaths?
Virtually everyone is susceptible. This is a novel virus, spreading in a human population with virtually 0% immunity.
With an R_0 of 2.4, approximately 60% of the population can be expected to contract the virus within a few months, unless mitigation measures are taken.
I think Diamond Princess is a pretty good petri dish scenario for testing that hypothesis. In fact, although there are still some ongoing cases so the data is not finalized, you can normalize by passenger/crew age and reach a final infection fatality rate estimate for the whole population.
Here's a tip: it still comes out to be 5-10x higher than the seasonal flu.