During this week we were presented with a problem on the growth of rat populations. The problem started by stating that there is two rats, one male and one female which boarded a ship and landed at an island in late December. The problem then went on and explained the constraints:
- The original female gives birth to six young on January 1st. She produces another litter of six rats every 40 days thereafter as long as she lives.
- Each female rat born on the island will produce her first litter of six young 120 days after her birth. She will produce a new litter of six rats every 40 days thereafter.
- Every litter has three males and three females.
- The rats have no natural enemies on the island and plenty of food. This means that no rats die.
At first, I was overwhelmed by the problem because it seemed to be a real difficult task to organize information with all the constraints I had to work through. I decided to take a different route and start up a Google Spreadsheet in order to organize information. I started with the very beginning which was late December where there was one mother and one father with a total of two rats. I input that information onto the spreadsheet and then skipped ahead to the next day (January 1st) when the original mother would have a litter of rats. That meant that three more females would be added along with the males which ended up with a total of 8. I also realized that the amount of males and females had to remain the same. I then skipped another 40 days when the original mother would have another litter which meant I would have to make a note to the side that the females born on January 1st are now 40 days old. I then took the litter and added that to the total which was 14. I then skipped another 40 days and the original mother had another litter again but this time the litter born on January 1st were all 80 days old and the litter born on February 10th were 40 days old. I then added the next six to the total which was 20 by March 22. In the next 40 days something else happens when the rats reach 120 days old. They then have babies for themselves. I realized that the litter from January 1st had 4 females total so that would mean that there are four mothers now. The February 10th babies are now 80 days old and the March 22nd babies are 40 days old. Now that there are four mothers, I would multiply 4*3 because there are 3 females/males and the values must remain the same. 4*3=12 and added on to 10 would make 22 male and females. Once I got that pattern down I used the pattern all the way to December 17th where I got my final answer.
https://docs.google.com/a/hightechhigh.org/spreadsheets/d/1b_uoS5frydM61P59tabRQunCg4lmbXL5D3QVP_POrsg/edit#gid=0
Answer
- The original female gives birth to six young on January 1st. She produces another litter of six rats every 40 days thereafter as long as she lives.
- Each female rat born on the island will produce her first litter of six young 120 days after her birth. She will produce a new litter of six rats every 40 days thereafter.
- Every litter has three males and three females.
- The rats have no natural enemies on the island and plenty of food. This means that no rats die.
At first, I was overwhelmed by the problem because it seemed to be a real difficult task to organize information with all the constraints I had to work through. I decided to take a different route and start up a Google Spreadsheet in order to organize information. I started with the very beginning which was late December where there was one mother and one father with a total of two rats. I input that information onto the spreadsheet and then skipped ahead to the next day (January 1st) when the original mother would have a litter of rats. That meant that three more females would be added along with the males which ended up with a total of 8. I also realized that the amount of males and females had to remain the same. I then skipped another 40 days when the original mother would have another litter which meant I would have to make a note to the side that the females born on January 1st are now 40 days old. I then took the litter and added that to the total which was 14. I then skipped another 40 days and the original mother had another litter again but this time the litter born on January 1st were all 80 days old and the litter born on February 10th were 40 days old. I then added the next six to the total which was 20 by March 22. In the next 40 days something else happens when the rats reach 120 days old. They then have babies for themselves. I realized that the litter from January 1st had 4 females total so that would mean that there are four mothers now. The February 10th babies are now 80 days old and the March 22nd babies are 40 days old. Now that there are four mothers, I would multiply 4*3 because there are 3 females/males and the values must remain the same. 4*3=12 and added on to 10 would make 22 male and females. Once I got that pattern down I used the pattern all the way to December 17th where I got my final answer.
https://docs.google.com/a/hightechhigh.org/spreadsheets/d/1b_uoS5frydM61P59tabRQunCg4lmbXL5D3QVP_POrsg/edit#gid=0
Answer