Copyright © 2013 by Modern Scientific Press Company, Florida, USA
International Journal of Modern Management Sciences, 2013, 22: 57-66 International Journal of Modern Management Sciences
Journal homepage:www.ModernScientificPress.comJournalsIJMGMTS.aspx
ISSN: 2168-5479
Florida, USA Article
Mathematical Model of Gh ana’s Population Growth
T. Ofori
1,
, L. Ephraim
2
, and F. Nyarko
3
1
Institute of Petroleum Engineering, Heriot-Watt University, HWU Edinburgh, UK
2
University of Mines and Technology, Faculty of Engineering, Tarkwa
3
University of Mines and Technology, Academic and Students Affairs Office, Tarkwa To whom correspondence should be addressed; E-Mail:adetundegooglemail.com
Article history: Received 18 March 2013, Received in revised form 19 April 2013, Accepted 23 April 2013, Published 25 April 2013.
Abstract: The purpose of this paper is to use mathematical models to predict the
population growth of Ghana. Ghana is a small country located in West Africa. It borders Burkina Faso, Ivory Cote and Togo and the Gulf of Guinea. The Exponential and the
Logistic growth models were applied to model the population growth of Ghana using data from 1960 to 2011. The Exponential model predicted a growth rate of 3.15 per annum
and also predicted the population to be114.8207 in 2050. We determined the carrying capacity and the vital coefficients
and are and , respectively.
Thus the population growth of Ghana according to the logistic model is and
predicted Ghana’s population to be 341.2443 in 2050. The MAPE of was computed as 16.31 for the Exponential model and 95.21 for the Logistic model.
Keywords : Exponential growth model, Logistic growth Model, Population growth, MAPE,
Carrying Capacity, Vital Coefficient.
1. Introduction
Projection of any country’s population plays a significant role in the planning as well as in the decision making for the socio-economic and demographic development. Today the major issue of the
world is the tremendous growth of the population especially in the developing countries like Ghana. A mathematical model is a set of formulas or equations based on quantitative description or
real world phenomenon and created in the hope that the behavior it predicts will resemble the real behavior on which it is based Glenn Ledder, 2005. It involves the following processes.
Int. J. Modern Mgmt. Sci.2013, 22: 57-66
Copyright © 2013 by Modern Scientific Press Company, Florida, USA
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1 The formulation of a real-world problem in mathematical terms: thus the construction of
mathematical model. 2
The analysis or solution of the resulting mathematical problem. 3
The interpretation of the mathematical results in the context of the original situation. A model can be in many shapes, sizes and styles. It is important to emphasize that a model is
not real-world but merely a human construct to help us better understand real-world system. One uses models in all aspect of our life, in order to extract the important trend from complex processes
to permit comparison among systems to facilitate analysis of causes of processes acting on the system and to make a prediction about the future. In this paper we model the population growth of
Ghana using the Exponential and the Logistic growth models.
2. Materials and Methods
A research is best understood as a process of arriving at dependent solutions to the problems through the systematic collection, analysis and interpretation of data. In this paper, secondary
population data was taken from World Development Indicator and Global Development Finance –
Google Public Data Explorer www.google.com.ghpublicdataexplore. The Exponential and Logistic growth mathematical models were used to compute the projected population values employing Maple.
The Goodness of fit of the models is assessed using the Mean Absolute Percentage Error MAPE.
3. The Exponential Growth Model
