than 1 indicates that the population of females is increasing, while a net reproduction rate less than one (sub-replacement fertility) indicates that the population of females is decreasing. Most populations do not grow exponentially, rather they follow a logistic model. Once the population has reached its carrying capacity, it will stabilize and the exponential curve will level off towards the carrying capacity, which is usually when a population has depleted most its natural resources. In the world human population, growth has been following a linear trend throughout the last few decades. Logistic equation The growth of a population can often be modelled by the logistic equation where = the population after time t; = time a population grows; = the relative growth rate coefficient; = the carrying capacity of the population; defined by ecologists as the maximum population size that a particular environment can sustain. As it is a separable differential equation, the population may be solved explicitly, producing a logistic function: , where and is the initial population at time 0. Population growth rate The world population growth rate peaked in 1963 at 2.2% per year and subsequently declined. In 2017, the estimated annual growth rate was 1.1%. The CIA World Factbook gives the world annual birthrate, mortality rate, and growth rate as 1.86%, 0.78%, and 1.08% respectively. The last 100 years have seen a massive fourfold increase in the population, due to medical advances, lower mortality rates, and an increase in agricultural productivity made possible by the Green Revolution. The annual increase in the number of living humans peaked at 88.0 million in 1989, then slowly declined to 73.9 million in 2003, after which it rose again to 75.2 million in 2006. In 2017, the human population increased by 83 million. Generally, developed nations have seen a decline in their growth rates in recent decades, though annual growth rates remain above 2% in some countries of the Middle East and Sub-Saharan Africa, and also in South Asia, Southeast Asia, and Latin America. In some countries the population is declining, especially in Eastern Europe, mainly due to low fertility rates, high death rates and emigration. In Southern Africa, growth is slowing due to the high number of AIDS-related deaths. Some Western Europe countries might also experience population decline. Japan's population began decreasing in 2005. The United Nations Population Division projects world population to reach 11.2 billion by the end