Problem are about chikungunya, a disease that arrived in the Americas in 2013 and spread rapidly in 2014. While seldom fatal, the disease causes debilitating joint pain and a high fever. In August 2014, a public challenge was issued to predict the number of cases in each of the affected countries. The winners, Joceline Lega and Heidi Brown, used a logistic model to make their predictions. Let N be the total number of cases of chikungunya in a country by week t, where t is measured since the first cases were recorded in that country. The progress of the disease in three Caribbean countries is represented by the logistic functions:

When the number of cases was still small, in which of these three countries did the number of cases grow at the largest continuous rate? What rate was that?

Dominican Republic = Dominica = Guadeloupe 539,227 1 + 176.8e-0.35t 3771 1+941.75e-0.32r 81,780 1+27,259e-0.32r