Prediction of the Number of Women Population in Medan City 2025 by Using the Leslie Matrix

Abstract

Population problems can cause problems, both in terms of political, economic, socio-cultural life, defense and security, as well as other aspects of life concerning the use of natural resources and the environment. By knowing the population growth rate, the Medan city government can implement a policy to anticipate social problems that may arise. This study aims to determine the number and rate of female population growth in the city of Medan in 2025. The Leslie matrix model is a model that can be used to predict the number and rate of female population growth. The step taken to predict the number of population p in the following year is to form a column vector whose entry is the initial number of population for each age class. Next look for n (t + p) which is the total population for the following year using the formula n(t+p)=Apn(t) where A is the Leslie matrix. Furthermore, to predict the population growth rate using the Leslie matrix is to find the positive eigenvalues λ of the matrix A. Based on positive eigenvalues λ, three cases occur, namely: 1) the population will tend to increase if λ>1; 2) the population will tend to decline if λ<1 ; 3) the population will tend to be stable if λ=1. Based on data analysis, the total female population in the city of Medan in 2025 is 1,576,294. Furthermore, the eigenvalues of λ=1,3673 which mean that the number of female populations in the city of Medan tends to increase.