# Exponential Growth Theory

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Introduction This research will investigate the use of exponential growth and decay model to explain different natural processes taking place in our world. The exponential growth and decay model is applied in many aspects of nature. Several natural phenomena follow the exponential growth and decay model. In order to understand important core processes occurring in the world such as population growth and radioactive decay, mankind needs to fully understand the exponential growth and decay model. Knowing this model helps to predict, namely, calculate approximately the future figures within a certain period of time. Therefore, this research aims to explain a world population growth in terms of exponential growth and show its importance. 2.…show more content…
when time is 0, y=C. Population Growth Since the rate of change of population is directly proportional to the population itself, the previous steps will be repeated to find population after a certain period time. P' = kP dP/dt=kP P(t) = 〖Ce〗^kt NOTE: P- population, P'- the rate of change of population, k - relative growth rate, t-time. For example, to find the Earth's population by 2050 we need only two distinct pairs of information: time and the corresponding population from the past. According to U.S. Census Bureau (2015) in 1950 the world's population was 2,557,628,654, and in 2000 world's population was 6,088,571,383. Using this data and applying exponential growth model, the population by 2050 can be estimated. The figure in 1950 is taken as initial population, so, t=0 when P= 2,557,628,654. In 2000, fifty years later t=50, P=6,088,571,383. In 2050 100 years later since 1950 t=100 and P(100) is to be found. Given: P(0)= 2,557,628,654; P(50)= 6,088,571,383 Find: P(100) - ? Solution: Main exponential equation: P(t) = 〖Ce〗^kt P(0)= 2,557,628,654 Substitute 0 instead of t, and 2,557,628,654 instead of…show more content…
However, the calculated number of people on the Earth by 2050 - 14 billion is more than the data provided by UN News Center (2013), which is estimated to be 9.7 billion. This is explained by the straightforwardness of an example calculations in order to the reader to clearly, easily understand the concept. Whereas, computations made by UN can be quite complex with consideration of death rates and other factors influencing future population on