Rat Pow

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Ian deGrouchy
Mrs. Psitos
Math IMP 2H
18 December 2007

Growth of Rat Populations
This POW is about the growth of a rat population over a year. Two rats, one male and one female, are put on an island that has ideal conditions for rats. The female rat has a litter of six rats the first day, and will have a litter every forty days after that. There are three important things to remember, and they are that the number of rats in every litter is six, three females and three males. Secondly, every female born on the island will have her first litter 120 days after she is born, and she will have a litter every forty days thereafter. Lastly, no rats will die in the first year.

I first decided to make a chart because I knew that I needed to keep track of the number of female rats having litters, the number of total rats born, and the number of female rats born that can have litters before the end of the year. This is what the chart looked like: DayNumber of rats having littersTotal number of rats

Number of female rats born that can have litters before the end of the year 1163
41163
81163
12142412
16174221
201106030
2412213266
281432580
321734380
3611398340

The days in the chart go up by forty because those are the only days that rats are being born. The lines represent when the numbers of females born 120 days earlier are able to have their own litters. For example, 120 days after the first litter is born, on day 121, the number of females able to have litters goes from one to four. This is because in the first litter, there were three females born. Another example is, on day 361 the females that were born on day 241 are able to have their own litters. This means that the amount of females able to have litters goes from 73 to 139 because I added the new 66 females. The last three dates have zeros in the last column because the females that were born on those days would not have litters by the end of the...
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