The Integration of World Population Growth and Calculus

by Hannah Westervelt

Submitted : Spring 2015

The purpose of this experiment was to determine how many years is required to reach the carrying capacity of world population. To do this the current population, growth rate, and carrying capacity was acquired. The approach utilized to attain this objective was using calculus through a logistic growth model of world population. This was done by first integrating the equation and then substituting the values into the equation. When the first equation was unfit for such a large population size, an improved equation was obtained and therefore used to find the growth of the population after one year. With this information, further investigation took place to determine how many years it would take to reach carrying capacity if the rate and carrying capacity remained the same. The results of this were that it would take approximately 193 years from the initial starting year which was 2015. This means according to this study, carrying capacity would be occupied at year 2208. However, with the variables growth rate and carrying capacity being applicable to change from many factors throughout time, it is difficult to precisely estimate the time required. For future and further investigation, the factors that affect and alter the variables should be taken into consideration and the adjusted variables should be utilized into the equation, making the results more accurate. 

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