Problem Statement
Two rats, one female and on male are landed on a island when they had abandoned ship when it anchored on a local dock. As they made their new home on the deserted island the female rat gives birth to a litter of six on January 1. Given ideal conditions what is an estimated rat population on the island a year later?
Given conditions:
Given conditions:
- The original female gives birth to a litter of six on January 1. She produces another litter of six every 40 days after that.
- Each female born on the island will produce her first litter 120 days after her birth. She will also produce a litter of six every 40 days.
- Every litter will have three males and three females.
- The rats have no natural enemies and their is an abundance of food on the island. So no rats will die in the first year
Process
One of the very first steps I took to tackle this POW was underlining/highlighting the key information given in the problem statement. After finding my guidelines, I drew out a table to organize my data. Once the table was ready I started my calculations. One of the strategies that I found that really helped me out was using a calendar to start at January first and count 40 days. After every 3 groups of 40 I added 3 new litters to the previous, I continued this pattern until I hit January first of the next year.
Below is my digitized draft of my final data table. It took a few tries to find a system and organized structure that could not only be read by myself, by others as well.
Below is my digitized draft of my final data table. It took a few tries to find a system and organized structure that could not only be read by myself, by others as well.
Solution
My solution for the 1 year anniversary of the two original rats breeding on the island did not match up to the answer that given to us ( 1808 rats), even though my solution does not match I am still fairly confident with my solution of 702. It wasn't until I got to the following September of the 1 year anniversary that I got a total rat population (1802 total) that I was more or less closer to the "solution" that was given.
Self ASSESSMENT/reflection
Organization was a mighty big factor in the outcome of this POW, organization was the backbone of the assignment. Throughout this POW I found myself struggling to understand what I had written down, it was not my handwriting, but the way I had labeled and divided my data table. After that I drafted out another table, a newer more organized table.
When it came down to finalizing my answer I had many doubts in my mind, for one the my answer did not match the one that given at the very beginning of this assignment. I did go back and re-calculate my data, but I still kept coming up with the same set of number, so from that point I decided that even if it is wrong my process is what matters. The process/steps taken to get my answer, right or wrong, are the elements that show my understanding of this assignment. Even if my answer is not correct I believe that my process show my growth as a mathematician.
When it came down to finalizing my answer I had many doubts in my mind, for one the my answer did not match the one that given at the very beginning of this assignment. I did go back and re-calculate my data, but I still kept coming up with the same set of number, so from that point I decided that even if it is wrong my process is what matters. The process/steps taken to get my answer, right or wrong, are the elements that show my understanding of this assignment. Even if my answer is not correct I believe that my process show my growth as a mathematician.