Growth Of Rats POW 
Ortiz 1
Yanelis Ortiz
Advanced Algebra
Ms.Curran
March 4 2014
The Growth of Rats
Problem Statement: When a ship sails across the ocean two rats are on board. A female and male are then left on a deserted island during late December. This island soon becomes the rats’ home. The number of offsprings that might be produced from this pair in a year should be estimated. One should make these assumptions when executing the problem.
❏ Every litter produces six young rats, and three of those six rats are females.
❏ The first rat that mates births six rats on January 1. Another litter of six young rats is produced every 40 days as long as the female rat is alive.
❏ After 120 days from their birth, females will have their first litter of young rats. A new litter will simultaneously be produced 40 days after the first.
❏ The rat population are not exposed to any negative factors on this island, such as: natural enemies, lack of resources, diseases, etc. Not one rat will die the first year!
By the following January 1st how many total rats will there be on the island? (Include the original pair that arrived on the ship).
Process: The first step that I took when solving this problem was to highlight all the important factors in the problem. For example: There is always an equal amount of male and females in every 6 litter, litters are produced every 40 days, etc. From the start I understood that
Ortiz 2
this problem is exponential because the rats’ population increases gradually forever. I then observed the days in a year in comparison to the amount of time between each litter (365 divided by 40 equals 9 cycles). New litters of rats, though will not automatically begin to reproduce after
120 days from birth because females can only produce litters. Originally the first litter of rats gives the island eight rats in total (counting the female and male parents). After 40 days there are
20 rats. From these rats there are 8 rats from the original
Yanelis Ortiz
Advanced Algebra
Ms.Curran
March 4 2014
The Growth of Rats
Problem Statement: When a ship sails across the ocean two rats are on board. A female and male are then left on a deserted island during late December. This island soon becomes the rats’ home. The number of offsprings that might be produced from this pair in a year should be estimated. One should make these assumptions when executing the problem.
❏ Every litter produces six young rats, and three of those six rats are females.
❏ The first rat that mates births six rats on January 1. Another litter of six young rats is produced every 40 days as long as the female rat is alive.
❏ After 120 days from their birth, females will have their first litter of young rats. A new litter will simultaneously be produced 40 days after the first.
❏ The rat population are not exposed to any negative factors on this island, such as: natural enemies, lack of resources, diseases, etc. Not one rat will die the first year!
By the following January 1st how many total rats will there be on the island? (Include the original pair that arrived on the ship).
Process: The first step that I took when solving this problem was to highlight all the important factors in the problem. For example: There is always an equal amount of male and females in every 6 litter, litters are produced every 40 days, etc. From the start I understood that
Ortiz 2
this problem is exponential because the rats’ population increases gradually forever. I then observed the days in a year in comparison to the amount of time between each litter (365 divided by 40 equals 9 cycles). New litters of rats, though will not automatically begin to reproduce after
120 days from birth because females can only produce litters. Originally the first litter of rats gives the island eight rats in total (counting the female and male parents). After 40 days there are
20 rats. From these rats there are 8 rats from the original