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Summary Math Analysis and Approaches - Using differential calculus to find the Best model that expresses growth of a given population$13.49
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Summary Math Analysis and Approaches - Using differential calculus to find the Best model that expresses growth of a given population
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Course
Math AA
Institution
This document contains an example of a high-scoring internal assignment of Mathematics Analysis and Approaches (Standard level). The mark received was 19/20. The topic discussed is Using differential calculus to find the best model that expresses growth of a given population.
As the name of this investigation suggests, this investigation will aim to use differential calculus to find a model
that best fits the data of a given population.
As I studied calculus in mathematics class, I was fascinated when I read an article that made me learn that
calculus isn’t just significant in maths and has an essential presence in the world of ecosystems and populations.
After undergoing further research I settled on a topic which is about calculating the population growth of
different species using differential calculus. As an IB biology and mathematics student, I decided to focus this
investigation on modelling growth which combines two subjects that I love, with those two subjects being the
ones that I am going to pursue in university as an undergraduate biomedical science student.
One important dynamical process in biology is the behaviour of organisms and their population, ultimately
influencing the growth rate. The growth rate differs from one species to another, but in every species,
reproduction is crucial for surviving. In fact, an important indicator of success is the growth of the species
population. This investigation will be fully focused on data from my local human population. The human
population growth is quite complicated when comparing it to other species/kingdoms. While the growth of some
bacterial populations occurs according to an exponential model, where for example one cell gives rise to 2, 2
cells give rise to 4, 4 cells give rise to 8, the human population does not follow a certain structure. Human
population growth does not occur at a normal growth rate and may be influenced by numerous factors such as
immigration and emigration, environmental factors, birth and death rate. Therefore, it does not always follow a
particular trend. For example, during the industrial revolution, the mortality rates started decreasing, thus, the
human population started growing rapidly. (Population Reference Bureau, 2009) However, in 2003, the human
population declined from 88 million people to 74 million people. (Roser et al., 2013). This indicates that Human
population growth does not occur at a stable rate.
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