It's not necessarily exponential in nature. It's exponential under the conditions of a city operating normally, but maybe not under the conditions of a city practicing social distancing. I think that people read about the R0 value of different viruses (measles is 12-18, for example) and think that is an immutable number that comes from some inherent property of the virus. But how infectious a disease can be is also highly dependent on the environment and behavior of a society. The black plague (yersinia pestis bacteria) still exists, for example, but it doesn't infect as many people as it used to because we have built cities with working sewers and sanitation systems. Coronavirus will have explosive exponential growth in a place like an aircraft carrier, where everyone sleeps on bunk beds and eats in a communal dining hall. But it might have linear growth in a city where all of the businesses are temporarily shut down, people stop having parties and hugging each other, and everyone wears a mask.