Question 49816: francisco was rasing afican spotted mice. they were unusual in that every two months the female had exactly two babies ---a male and female. when these babies were two monthes old, they had their first babies and continued to have them every two months after that.
Francisco began with one pair of spotted mice on jan. 1 1998 and his parents made him sell all that he had on jan.1 2000, just after more babies were born since none of the mice had died, he had quite a few How many?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! francisco was rasing afican spotted mice. they were unusual in that every two months the female had exactly two babies ---a male and female. when these babies were two monthes old, they had their first babies and continued to have them every two months after that.
Francisco began with one pair of spotted mice on jan. 1 1998 and his parents made him sell all that he had on jan.1 2000, just after more babies were born since none of the mice had died, he had quite a few How many?
..................................NUMBER OF MICE
..............................MALE.......FEMALE......................TOTAL
ZERO DATE..1-JAN-98............1=2^0..........1=2^0...................2=2^1
AFTER 2 MONTHS=2*1 MONTHS......1+1=2^1.......1+1=2^1..................4=2^2
AFTER 4 MONTHS=2*2 MONTHS......2+2=2^2.......2+2=2^2..................8=2^3
AFTER 6 MONTHS=2*3 MONTHS......4+4=2^3.......4+4=2^3..................16=2^4
.........................................................................
...........................................................................
ON 1-JAN-2000
AFTER 24 MONTHS=2*12 MONTHS.....=2^12..........=2^12................=2^13
--------------------------------------------------------------------------
TOTAL NUMBER OF MICE............=2^1+2^2+2^3+2^4........+2^13...
THIS IS A GEOMETRIC PROGRESSION WITH FIRST TERM=A=2.....COMMON RATIO=R=2
AND NUMBER OF TERMS = N= 13
S=A(R^N-1)/(R-1)=2{2^13 -1}/(2-1)=2^14-2=16382
|
|
|
