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?

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