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3/4 pts Eduardo... Bertha corrected your paper, but you did not correct hers which made her get behind in her asignments... Your paper still has some things to be corrected... Please do. A mathematical model is a description of a fact or problem using mathematics as words, the job of a model is to describe a real life problem in a way that it makes sense in the mathematical world. The main idea behind the models its to work the real life problem by using mathematics and since we know a lot of tools in this field, bringing the problem in mathematical __terns__ ** terms​ ** allows us to use this tools than we have which makes it easier to solve the problem.

The population growth is a subject that many people over the years have been trying to understand, by the day we have a lot of different models that represents the **(** __the__ **)** way in which a population grow. Even though there exist so many models we can separate them in two big stacks, the first type are called "unlimited growth" and the second type is called the "limited growth". The first model __its__ **it is** based on the idea that an isolated population always grow, and the really objective with this model is to try to calculate how fast or what parameters determinate the rate in which a population grow. The first person to came up with this model was Tomas Malthus and the basic equation of the population grows was the following:

Where Pn is the population at some n time parameter and r was a constant that is related to how fast the population growth, the determination of this constant is really hard since a lot of parameters are involved. The following picture is an example of how population grows depending on the R constant:  As you can see those curve all or exponential, this means that as larger is the amount of population the R coefficient will be bigger, in other words Pn+1/Pn it's not constant.
 * || [[image:http://www.arcytech.org/java/population/images/image42.gif width="80" height="24"]] ||

The second type of model stipulates that the population over times tends to a number, this means that the population grows until certain point and after that he starts to oscillate around a constant number, in this model not only we try to calculate the rate in which the population grows but until what point it grows and how does it oscillate around that constant number. It has different models but the most general one is express in the following equation:

P(n+1) = A(pn) - B(pn2) were A >> B and both are constant

You can see from this equation that if pn grows too much the __tern__ ** term ** (pn2) will get bigger faster than pn so the population wont be growing. The next picture is an example of how population growth function are depending on a factor R which is calculated using the constant A and B: 

Both models deserve credit, my personal opinion is that both models are right under the right population. For example if you are talking about rabbits in an island, it is obvious that past some point they wont be able to reproduce because they wont have space or because they would have eat more food than the island can produce, under this circumstances it is obvious that the rabbits population wont be able to grow past some point, you will have to consider the evolutionary aspect in this example but since __i__ ** I ** am talking about an island __i__ ** I ** am assuming it wont be that big in order for evolution to form a big part on the population growth part. If you are talking about a big space for example the universe and you are talking about a population such as human __i__ ** I ** will have to say that the first model is probably more accurate than the second, __i__ ** I ** don't see how the human race can at some point extinct if the technology is increasing as it is, it is very possible that this technology in some future allows us to created that balance between nature and human, as for the factor of space we can **´** t or can not assure that we live in a finite world. The evolutionary factor also comes in play in this second example, it is possible that the human in the next thousand years adapt to a new form of life, so in that case we would have more spaces to expand too.