Abstract

Mathematics is a tool that can be used to solve everyday problems. One such problem is garbage (waste). The problem of determining the time when all waste can be transported is a mathematical modeling problem that can be modeled by arithmetic sequences. The purpose of this study is to obtain a mathematical model that can be used to determine the time such that waste can be transported entirely to the Final Disposal Site. In this modeling two types of data are used, namely data on the volume of waste and the volume of garbage transported in Purwokerto City from 2008 to 2017. The obtained model was stated to be very good because the volume of waste model and the volume of transported waste model had MAPE below 10%, respectively of 2.41% and 4.82%. With arithmetic sequences, it is predicted that in 2037 all rubbish in Purwokerto City can be transported to the Final Disposal Site. In addition, from the modeling process, three mathematical problems were obtained namely determining the time of occurrence of the break event point, modeling with averages of the differences, and analysis of the differences in arithmetic sequences.