For the time period 1500 < t < 2020 the following function was chosen as an interpolation approach:
Total population( t ) = b × exp( a × t / | c - t | ), with a, b > 0, c > 2020
The parameters a, b, c were decided according to the method of the smallest squares under the auxiliary condition that the most current total population as exact is accepted. The interpolation function represents a development of the compensation from most different statistics of total populations (e.g. www.census.gov/ipc/www/popclockworld.html, www.census.gov/ipc/www/img/worldpop.gif, www.ecopop.ch, www.weltbevoelkerung.de, www.un.org/esa/population/unpop.htm, www.bib-demographie.de, http://members.aol.com/jspanalysis/analysis/wachst4.htm). For the animation shown here 34 times were used and in a second the development of 100 years is represented.