After analyzing the data, they realized that the population growth of the Moonlight Serenade could be modeled using a system of differential equations. They used the logistic growth model, which is a common model for population growth, and modified it to account for the seasonal fluctuations in the population.
The team had been monitoring the population growth of the Moonlight Serenade for several years and had noticed a peculiar trend. The population seemed to be growing at an alarming rate, but only during certain periods of the year. During other periods, the population would decline dramatically.
The logistic growth model is given by the differential equation: