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Pt1420 Unit 1 Exercise 1

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Kill Rate 2
In the latest press conference held by the UN, it has become clear that as the zombie pack has grown, they have started to split up. Consequently, the zombies are no longer only killing the humans at a rate of 5 per day. According to the UN press conference, the new rate of change of the human population can be modelled with the following equation. This equation shows that the rate of change of the human population can be expressed by minus the population of zombies. Consequently, this new model predicts that the zombie population will grow exponentially. It is possible to use this equation to find out how quickly the human population is changing for any number of zombies. For example, if there are 50 zombies, the rate of …show more content…
When time is 0, it has already been stated that there are 9999 humans. Therefore, these values can be substituted into the equation and it rearranged for A. Therefore, the population of humans can be modelled by the following equation. Thus, the population of zombies is modelled by, . Both of these can be graphed as follows. Figure 2. Populations of both zombies and humans over time.
Using figure 2, it can be seen that the time that it takes the zombies to overtake the human population has drastically decreased, compared to the previous model. In fact, according to the figure, it will only take 9.21 days before all the humans are turned into zombies. As a result, this new model predicts that the zombies would pose a massive threat if they were to leave the island, as they would be able to quickly overrun any number of humans.
This model has a number limitations. The most obvious one is that it assumes that the rate of change of the zombies is constantly increasing. This would not be possible, because as time passes people would get better at avoiding zombies. Consequently, the longer the outbreak lasts for the slower the rate of the zombies change. Thus, this model at best would be able to predict the outbreak during the first few

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