Pow 15

 Essay regarding Pow 12-15

POW 12-15 Growth of tipp populations Difficulty Statement This challenge is composed of the growth of a verweis population throughout one year via 2 rodents. Four presumptions for this issue were made: Each new liters is composed of six rats; 3 males, several females. The initial pair offer birth to 6 rats on the first day and then ever 40 days and nights after. There is a 120 time " gestation" period before a newborn tipp can duplicate. After this pregnancy period the rats will offer birth every 40 times. Also over the course of a year no rats die. The key problem is how many rodents are there following one year. Method In order to solve this problem I first focused on getting a solution for the amount of rats. Formerly I had designed to use a huge sheet of poster table paper to draw out the family tree. Nevertheless quickly realized that this would be quite impractical. Then i settled on an identical but more effective method. Through this method I actually focused on the 10 l that the initial parents created. The 10 liters comes from the fact there is 365. 25 days in a year and the mother or father liter develop every 40 days by day actually zero. Meaning that they are going to have a liter in day 0, 40, 70, 120, one hundred sixty, 200, 240, 280, 320, and 360. I began on the day fish hunter 360 liter and worked in reverse. After finishing this method We compiled the information in a schedule. From which I had been able to sum each period of rat births. Your data collected in family tree technique is shown in the following info table: Couple: Original D0 D40 D80 D120 D160 D200 D240 D280 D320 D360 Quantity 0 two 6 40 80 a hundred and twenty 160 200 240 280 320 360 Total Sum after labor and birth 2 2 6 almost 8 6 16 6 twenty 24 forty-four 42 eighty six 60 146 132 278 258 536 438 974 6 834 1808 six 1808

six 6 18 6 18 18 18 18 18 72 18 18 18 126 seventy two 18 18 180 126 72 18 396 180 126 72 836 438 258 132

6 six 6 18 18 18 54 6 18 18 36 6 18 18 6 six

I then found the routine that emerged in the uppr data stand interesting. And so i decided to check into it further. At first We looked at the graph from the sum following birth to find out what kind of relationship it was.

Sum vs Day

2150 1800 1600 1400 twelve hundred 1000 800 600 400 200 0 0

55

100

150

200 Series 1

250

300

three hundred and fifty

400

As clearly demonstrated the growth is exponential. I then tried to obtain a model with this data yet could not receive anything that match it flawlessly, which is what I was aiming for. So I shifted to looking for relationships inside the data. We looked at the ratios and differences between days plus the sums, and rats born. But was not able to come up with anything at all. I then attempted to look at other relationships among sterile rats, reproducible rats, and the total before and after birth. Sum following birth # rats reproducable sum just before birth # sterile a couple of 8 a couple of 2 0 14 2 8 six 20 two 14 doze 44 almost eight 20 12 86 18 44 35 146 twenty 86 sixty six 278 forty-four 146 102 536 eighty six 278 hundranittiotv? 974 146 536 390 1808 278 974 696

Solution My own solution just for this problem was 1808 mice at the end of just one year. I believe that this option is correct because of the pattern noticed when looking at the compiled info table. Also because after creating the table shown over (last page) it was logical that that was just how it figured out. Through the span of working on the situation I looked over various ways of solving and trying to find patterns and became familiar enough while using growth of the rats that my solution appears to be completely logical with no questions or discrepancies kept open. Generalizations In order to generalize this problem My spouse and i first searched into jumping right to an precise formula nevertheless quickly found that doing so would be very improbable. And so i then looked into a recursive function that could model the citizenry. Looking at the expansion logically I recently came across that the initial 3 date ranges 6 mice were due. Then for the 4th day (120) the quantity of rats delivered were gonna be 6+ the number created 120 days and nights earlier, or perhaps 3 dates back. Then in the event you continue this kind of a recursive function comes forth; such that:

two

U0 = 6 U1 = 6 U2 sama dengan 6 U n = (3(U n в€’ a few ) & 3(U n в€’ 4 ) + 3(U and в€’ your five ) &... + 3(U n в€’ n ) )+ 6

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