Asia Pacific Journal of Multidisciplinary Research, Vol. 3, No. 2, May 2015 _______________________________________________________________________________________________________________ 17 P-ISSN 2350-7756 | E-ISSN 2350-8442 | www.apjmr.com Mathematical Model to Extrapolate the Population of Ghana: An Application of Newton‟s Divided Difference Formula Richmond Opoku-Sarkodie, E. Acheampong, Patrick Enu, Amadu Bokoum, F. A. Gardiner, T. A. Manu Methodist University College Ghana patrickenu@gmail.com Date Received: January 22, 2015; Date Revised: February 19, 2015 Abstract - This work presents the derivation of a mathematical model for extrapolating the population of Ghana using Newton’s divided difference formula. Newton’s divided difference formula was used because of the uneven time intervals at which the population census was conducted. A simulation was done using mathematical software to estimate the parameters in the derived model because the exact solution was quite difficult. The model was able to predict the population of Ghana with a residual percentage error within 10%. We will therefore recommend the usage of this model to be used for countries in which the population censuses were conducted at uneven time intervals as was the case with Ghana. Keywords: extrapolation, population, Newton’s, divided difference formula, Ghana INTRODUCTION Ghana has had uneven population census over the past few years until 2010. This has made socio- economic and demographic planning very difficult for the country – Ghana, more especially activities in the services sector (electricity, water, housing etc). The difficulty in socio-economic planning and demographic planning are due to the incorrect predictability of the population size within the decennial periods based on exponential growth model. This study, therefore, seeks to develop a population model for Ghana using Newton‟s Divided Difference Formula which will be used to predict Ghana‟s population figures with a greater amount of accuracy. One of the major problems facing the world today is excessive population growth in relation to the development of the natural resources of the world. The composition and growth of the population of any country have a direct bearing upon its socio-economic and demographic developments. The most important fact underlying the current population debate in developing countries and for that matter Ghana is that while population is increasing to an uncontrollable size, economic resources are very limited. It is therefore important to study population issues to be able to control population growth so that the desired socio-economic and demographic developments can be realized. Most countries including Ghana conduct population census periodically to ascertain the population growth of their country at a particular point in time. This is to aid research, business marketing, and national economic and financial planning. The first census in Ghana was conducted in 1891 by the then British Administration. Since then population censuses were conducted every ten years in Ghana. Ghana has experienced population census in 1891, 1901, 1911, 1921 and 1931 when the second World War discontinued the series and as a result there was no population census conducted in the year 1941 (Ghana Statistical Service 2010 Population and Housing Census National Analytical Report, 2013). After the Second World War a population census was conducted in 1948, the last census organized by the then British Administration. These earlier population censuses were conducted in the same years as censuses in the United Kingdom. After Ghana‟s independence in 1957, the country adopted the United Nation‟s recommendation to conduct population censuses in years ending with zero or closer to zero. So, the first post-independence population census was conducted in 1960 and the second in 1970. Between these periods the population of Ghana grew from 6.7 million in 1960 to 8.6 million in 1970. This gave an inter-censual growth rate of 2.4% per annum. There was no population census in