POW 6: Growth of Rat Population
In the "Growth of Rat Population" problem, us students were given a problem to figure out how many rats were on an island after a year after repopulating. We were given a few facts in order to help us find the answer.
These facts are:
- Two rats, one male and one female board a boat and find themselves on a deserted island.
- The original female gives birth to six babies on January 1st. Three of them are male, three of them are females.
- Following the first birth on the island, the original female has 3 male and 3 female babies every 40 days
- Each female rat born has her first group of babies 120 days after she is born. Like her mother, she always births 3 male and 3 female rats.
- After a rat has babies for the first time, it will produce a new litter of 6 babies every 40 days
- None of the rats die
How many rats are on the island on January 1st of the next year
These facts are:
- Two rats, one male and one female board a boat and find themselves on a deserted island.
- The original female gives birth to six babies on January 1st. Three of them are male, three of them are females.
- Following the first birth on the island, the original female has 3 male and 3 female babies every 40 days
- Each female rat born has her first group of babies 120 days after she is born. Like her mother, she always births 3 male and 3 female rats.
- After a rat has babies for the first time, it will produce a new litter of 6 babies every 40 days
- None of the rats die
How many rats are on the island on January 1st of the next year
In order to solve this problem, I went through the process of making a table. I divided the year of 365 days into 40 day increments. This is due to the fact that the rats reproduce every 40 days or 120 days(40 goes into 120, so the 40 day increments work). The first few increments of 40 days were very easy to figure out due to the fact that only the original female was reproducing. Up until day 121, the only mother producing babies was the original female. This caused an increase of 3 males and 3 females each time. Once solving past day 121, I came up with a new strategy. Every single time a day increment of 40 came up, I took the amount of females that had babies last time, and added it to the amount of females born 120 days ago. I took that sum and multiplied it by 3. For example on day 321 I did the math equation 3(43+30) to find out the amount of females born that day. I added 43 because that is the amount of non first time females ready for birth and the 30 because that is the amount of females born 120 days ago ready to give birth for the first time. Once I got the answer of 3(43+30)=219, I added 219 to the existing female rat population (268 at the time), and got 487. I did the same for the male because there will always be the same amount of males as females. I took the sum of the males and females at the time and recorded the total for that day.
Once I recorded the amount of babies on the 361st day, I knew I had the answer. This is due to the fact that 361 is the last day for reproduction. I got the answer of 904 males and 904 females for a total of 1808 rats! Once I came up with a system for solving the more complex days of birth, doing the rest of the problem was pretty simple. Due to keeping my work (semi) organized, and checking over it a few times,(and with Mr. Corner) I am pretty confident my answer is correct. Now it is time to introduce rats on the island!
Once I recorded the amount of babies on the 361st day, I knew I had the answer. This is due to the fact that 361 is the last day for reproduction. I got the answer of 904 males and 904 females for a total of 1808 rats! Once I came up with a system for solving the more complex days of birth, doing the rest of the problem was pretty simple. Due to keeping my work (semi) organized, and checking over it a few times,(and with Mr. Corner) I am pretty confident my answer is correct. Now it is time to introduce rats on the island!
I think I deserve a grade of 10 out of 10 because I was able to come up with an answer on my own as well as giving people a push in the right direction with their strategies. I used two Habits of a Mathematicians in particular that really showed in my work progress. I already talked about how I "Stayed Organized", but I also was able to solve the problem by "Being Systematic". If you find out a simple repetitive strategy in order to solve a more complex problem, it makes it a lot harder to make a mistake. Also, if you make a mistake, it is somewhat easy to see where you made it, then go back and fix it.