The exponential function is a terrifying beast. Any alternatives we don't know now are irrelevant. There is a reason why NYC is bracing for impact: a tsunami of new cases are about to slam into the healthcare system.
Usually Hacker News middlebrow skepticism is just in poor taste. On this topic, it is foolish and farcical. One of our doctor friends is already telling us that her hospital is under stress and she's not in one of the hardest hit states.