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wwehh

IA
Math Exploration on Population Growth

So i've decided to switch my Math IA to population growth instead.

I know that there is already an equation created for population growth and this confuses me because would that mean my ia would only consist of plugging in numbers into an equation and then simply manipulating it a little (because I want to find the optimal population in a country)? :/ Like, what else am I supposed to do?

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IB was explained to me as a program "where all the classes can intermingle with one another".

Playing off this idea, perhaps you could include the effects of the population gain/loss on the location. For example, you could consider how losing 5 million people could affect the price of food. (supposing that X percent of the country are farmers) You can expand this beyond just finding the optimal population.

PM me with questions

Best of luck

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In an older set of math IAs back when they were assigned and you didn't have to come up with your own topic, there was a SL IA where they gave you some population data and it was up to you to come up with an equation for population growth exploring different types of functions that you could use to model the population growth. You could try doing something like that. Even though there is an equation for population growth that's pretty standard, maybe the population you pick could be best modeled by some other function (a higher-degree polynomial, regression curve, or use of some trigonometric functions just to give a few ideas). You could look at how well the population fits the model you develop by performing some sort of error analysis, and then using whatever function you choose to find an optimal population, determine the population in the future, or whatever you wish to do.

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A common model for population (and in my opinion, the most precise one) is the logistic model equation. It is not extremely hard to derive if you know a bit of integration, and it should prove to be challenging and interesting enough to model growth in a more "developed" society (in which we can think of constraints to population such as resources, and people having fewer children, and many other factors).

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