This mathematical report will be focused on the study of populations of animals that live in the Central Desert. Florence is an ecologist, that is studying and collecting data in regard to the population of the two animals; the blue lizards and the purple parrots. The data was collected for 20 months in total (0 – 19 months). The data collected by the ecologist can be modelledmodeled by many functions such as the Periodic functions, Polynomial functions, Quadratic functions, and etc. When the data is plotted on a specialized software (Desmos), the data can be easily modelledmodeled by the Periodic function. A periodic function such as Cosine and Sine function, are functions that have the same values at certain intervals, and also are repeated forever. Periodic functions are used in today’s world to model populationspopulation growth of the animalanimals, people and etc, unlike. Unlike other functions, periodic functions can predict the population of animals, people and etc., based on the previous data collected. Therefore, the data collected by the ecologist, Florence, can be modelledmodeled by periodic function, as it can be modelledmodeled by the function and can also be used to predict the population of animalanimals based on the data that she has collected based on the animal. In this mathematical report, the data will be modelledmodeled using a periodic function, it may involve methods of substitutions, trial and errors and etc. The closest and accurate functions produced from the periodic function will be used as an approximation of the data collected, thus allowallowing the ecologist to predict the population of animals.