The lazy nature of learning is an obstacle in teaching and learning activities. The higher level of laziness will reduce the students learning achievement. This problem has motivated the author to make a mathematical model of student learning's lazy nature and analyze it. The lazy nature of learning is modeled to a discrete-time system with , denotes a state vector of the lazy nature, represents an input vector system in time, and denotes a coefficient matrix of and . The optimal quadratic control method is applied in the model to analyze the system's stability and give the interpretation of the model based on the graphics info obtained during the simulation process. The feedback controller is obtained as a result of optimizing the quadratic objective function. a feedback controller's existence makes the lazy nature of learning physics students decrease from time to time, and the system becomes stable.
<p class="06IsiAbstrak">The rapid population growth in the DKI Jakarta area has an impact on its population and creates an unfriendly environment. The author is motivated to analyse the effect of the population growth rate in DKI Jakarta over the next 10 years. The process of estimating population growth is calculated by a mathematical model called the logistic model. The logistic model is the model that developed by differential equation like the following . This model illustrates that population growth is determined by the difference between the number of births and deaths of the population. In addition, an analysis of the resulting environmental impact and the impact of its handling will also be discussed. Based on estimation, the population in DKI Jakarta Province in 2022 is predicted around 10,636.685 people and it will reach 10,938.900 in 2030. It means there will be a 3% increase in population from 2019 to 2030 in DKI Jakarta Province. These values increase annually and they are predicted to have an impact on increasing the traffic congestion by 3%, from 70% to 72.1%. Another result has also occurred in air pollution. The average of air pollution increasing by 3%, from 39.6 to 40.79 . These two factors show that the increase of population growth will have an impact on increasing the average traffic congestion and the percentage of air pollution in DKI Jakarta.</p><p class="06IsiAbstrak"> </p><p class="06IsiAbstrak">Pertumbuhan penduduk yang sangat pesat di wilayah DKI Jakarta memiliki dampak pada populasinya serta menciptakan lingkungan yang kurang ramah. Hal ini memotivsi penulis untuk menganalisis dampak dari laju pertumbuhan penduduk di DKI Jakarta selama 10 tahun mendatang. Proses estimasi pertumbuhan penduduk dikalkulasi mengunakan pemodelan matematika yang bernama model logistik.Model logistik adalah sebuah model matematika yang dikembangkan menggunakan persamaan differensial sebagaimana berikut . Model logistik mengilustrasikan pertumbuhan populasi penduduk sebagai selisih antara jumlah populasi yang lahir dengan jumlah populasi yang meninggal. Selain itu juga, akan dipaparkan mengenai dampak pencemaran lingkungan yang mungkin akan muncul di waktu yang akan datang. Berdasarkan hasil estimasi diperoleh prediksi jumlah penduduk di Provinsi DKI Jakarta pada tahun 2022 sebanyak 10,636.685 jiwa dan pada tahun 2030 akan mencapai 10,938.900. Hal tersebut berarti akan ada peningkatan sekitar 3% penduduk dari tahun 2019 hingga tahun 2030 di Provinsi DKI Jakarta. Nilai pertumbuhan populasi tersebut meninggkat setiap tahunnya dan diprediksi dapat meningkatkan kepadatan lalu lintas sebesar 3%, dari 70% menjadi 72.1% di tahun 2030. Hasil lain yang diprediksi akan terjadi ialah peningkatan rata-rata polusi udara sebesar 3%, dari 39.6 menjadi 40.79 pada tahun 2030. Kedua faktor ini menunjukan bahwa peniongkatan jumlah populasi penduduk di Provinsi DKI Jakarta dapat memberikan dampak pada peningkatan rata-rata kepadatan kendaraan dan polusi udara di Provinsi DKI Jakarta.</p>
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