Mathematics encompasses several domains of society and has been developed over the years. British economist Thomas Malthus promoted a theory in 1798 with a mathematical model for population growth. Malthus argued that the rate of population growth at any given time is proportional to the total population at that time. However, Belgian mathematician Pierre Verhulst found limitations in the model developed by Malthus and presented a new equation suggesting that a population will grow to a sustainable maximum, that is, it tends to stabilize. The analysis of a city's population growth is important to characterize the social, economic, historical and political aspects. In this sense, I connected an important aspect of my city to the application of mathematical models. This project aims to apply the two mathematical models, Malthus and Verhulst, to examine which is the most effective to describe the population growth of Florianópolis Santa Catarina (SC), Brazil from 2012 to 2020. My hypothesis, related to the comparison of models, suggests that the Verhulst model will present results closer to the real population data, due to the greater complexity of the formula for including the value of the population growth rate. Applying the formula of the models to the values ​​of the real population, the constants 'k' will be obtained, which made the comparison possible. The construction of graphs will be fundamental to visualize which of the values ​​obtained for the constant k, in the two models, is close to the values ​​of the real population. In order to obtain precise results, the least squares method was applied to the values ​​that will be obtained through the Verhulst model. So, making the comparison, the hypothesis will, in fact, be confirmed. The Malthus and Verhulst models satisfactorily described the real process of population dynamics in Florianópolis, SC, Brazil, for the period 2012-2020. However, the values ​​that the Verhulst model will provide will be closer to the values ​​of the real population of Florianópolis. Key words: Mathematical models, population growth.