Eh, so far only 600 of the 4800 member crew has tested positive. That should still be comfortably in the "mostly exponential" territory.
If, as is most likely, they're PCR tests for viral RNA, then they'll only detect active (or recently-active) infections. So anyone who's gotten-over an infection, symptomatic or not, will test negative. The number of infections reported here is a floor on the actual number who have been infected – which could be 2x, 4x, or more.
If instead these are antibody tests, then they're only indicating 600 total infections. But that kind of test is less likely here: such tests are not very useful for diagnosis of active infections, as they only turn positive late in a case. They could be useful for tallying past infected status – but there's a lot of rumbling that early antibody tests haven't been as reliable as hoped.
The best current data on the IFR for 20-40 year olds is low enough that you might not get any deaths out of a ship-wide infection[0], so you don't have the same "Where were all the dead bodies if this ran through the population earlier?" question you do for cities and countries.
The current estimate of the recovery time is around 25 days, and the date of exposure is believed to be March 5th. Assuming we're looking at an exact snapshot of infections today, that gives you March 23rd as the day everyone recovered on the ship was infected by, about 18 days after the first exposure. Assuming some small number (~10) were initially infected, that would only require a doubling period of ~2 days, which is shorter than seen elsewhere, but you're also in an ideal environment (close quarters, communal living) for spread.
I don't know if I believe that to be what happened here, but we should hopefully be able to determine it from the data after the fact with further monitoring and testing.
[0] There's been one, and you could have up to around 6 or 10 while being consistent with the current data; more than a couple dozen would raise a lot of questions.