POW #8: Rat Reproduction
The question that this problem asked was if there were 2 original rats on an island, then we are given these conditions:
So to start off this problem the first attempt I had was to basically make little serbs of the beginning female going all the way to the last rat but as I was doing this there were to many rats to keep track of and it became to difficult. So then I Decided to only keep track of the females and then in the end when I had my answer I would just multiply it by 2, so that it would give me my final answer. So to start off I counted every 40 starting from 1 to 360 because 360 days is a whole year which is what we are trying to figure out. With the numbers from 1c 1-360 I knew that she has 30 females a year and from there I wrote out 30 f's then under that I knew that each of them would have at least 3 females so I added that under neath each F. Now I had to figure out when the newborn female rats would have their litter because they have to wait 120 days after their birth to give birth. So I then did the math and 120 days equals 4 months which means that the rats would have 8 months(240 days) to give birth. and with those 8 months they are able to give birth to 6 litters and produce 210 females. So I have so far:
Original F = 30 kids
30 kids= 210 kids
Then I saw that after the 120 days they were born they had 120 days (4 months) to reproduce before the following January. So within those months each rat is able to have 4 litters with 3 females in each one. So I then knew that if each rat had 12 females then I would just need to multiply that by 210 and I got 2520 more rats so as a total number of rats I got is 2760 but I have to multiply the number by 2 because all the math I did was only for the females so I have to include the entire number of rats. 2760*2= 5520 plus the original rat parents So the final number I got was 5522 rats.
I am questioning my answer because I'm not sure if some of the "grand rats" are even able to reproduce because the year is already up since the original rats took the whole year to reproduce and if one of the original kid rats were able to produce cause they would have to wait 120 days before reproducing again.
- the original female gives birth to 6 young on january 1. She produces another litter of 6 rats every 40 days thereafter as long as she lives.
- Each female rat born on the island will produce her first litter of 6 young 120 days after her birth
- Every litter has 3 females and 3 males.
- No rats will die the first year
So to start off this problem the first attempt I had was to basically make little serbs of the beginning female going all the way to the last rat but as I was doing this there were to many rats to keep track of and it became to difficult. So then I Decided to only keep track of the females and then in the end when I had my answer I would just multiply it by 2, so that it would give me my final answer. So to start off I counted every 40 starting from 1 to 360 because 360 days is a whole year which is what we are trying to figure out. With the numbers from 1c 1-360 I knew that she has 30 females a year and from there I wrote out 30 f's then under that I knew that each of them would have at least 3 females so I added that under neath each F. Now I had to figure out when the newborn female rats would have their litter because they have to wait 120 days after their birth to give birth. So I then did the math and 120 days equals 4 months which means that the rats would have 8 months(240 days) to give birth. and with those 8 months they are able to give birth to 6 litters and produce 210 females. So I have so far:
Original F = 30 kids
30 kids= 210 kids
Then I saw that after the 120 days they were born they had 120 days (4 months) to reproduce before the following January. So within those months each rat is able to have 4 litters with 3 females in each one. So I then knew that if each rat had 12 females then I would just need to multiply that by 210 and I got 2520 more rats so as a total number of rats I got is 2760 but I have to multiply the number by 2 because all the math I did was only for the females so I have to include the entire number of rats. 2760*2= 5520 plus the original rat parents So the final number I got was 5522 rats.
I am questioning my answer because I'm not sure if some of the "grand rats" are even able to reproduce because the year is already up since the original rats took the whole year to reproduce and if one of the original kid rats were able to produce cause they would have to wait 120 days before reproducing again.