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).
The Essay on Litter Problem/Solution
Recently, residents who live near the Buheirah Corniche have increasingly faced the problem of people leaving litter which often ends up in the lagoon. To put an end to the littering, Sharjah Municipality and the semi-private environmental company Bee'ah are coordinating to draft a new law to punish people who litter. The current fine for littering ranges from Dh200 to Dh250, but the new draft law ...
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 amount and 12 more rats from the litters that the three female rats produced after 120 days. This strategy worked for me when solving this problem because it allowed me to visualize the numbers of rats, arranged by the number of litter. I kept on doing this strategy until my final answer was achieved. Solution: My answer was achieved by following this system of steps.
The first litter of rats produces 6 young rats (who cannot produce litters until after 120 days).
After the second litter there are six young rats, six 40 days old rats, 0 eighty days old rats, and the original female and male rats. This occurs because the original female rat continues to breed every 40 days after her first litter, but the first litter does not reproduce just yet. After the third litter of rats there are 24 young rats, six 40 days old rats, six 80 days old rats and in total eight adult rats (including the original rats).
The fourth litter provides the island with 42 young rats, 24 forty days old rats, and 6 eighty days old rats, and 14 adult rats. Fifth litter there is 60 young rat s, 42 forty days old rats, 24 eighty days old rats, and 20 adult rats. Sixth litter there is 132 young rats, 60 forty days old rats, 42 eighty days old rats, and 44 adult rats. Seventh litter there is 258 young rats, 132 forty days old rats, 60 eighty days old rats, and 86 adult rats. Eight litter there is 438 young rats, 258 forty days old rats, 132 eighty days old rats, and 60 adult rats. Ninth litter there is 834 young rats, 438 forty days old rats, 258 eighty days old, and 278 adult rats.
