if i buy 2 mouse on january 1 1998 which is 1 male and 1 famale the female mouse gives birth every two month 1 male and 1 female the same circle happens with all the female mice for 2 year i need the know the total number for mice because i need to sell them on january 1 2000
make a chart
Jan 1/98 ...1 male....1 female = 2 mice
Mar 1/98 ...2 males...2 females = 4 mice
(the 1 female produced a new male and a new female, add these to what you had)
May 1/98 ...4 males ... 4 females = 8 mice
(the 2 females produced 2 new males and 2 new females, add these to get 4 males and 4 females)
July 1/98 the 4 females produce 4 new males and 4 new females, so now we have
8 males and 8 females, for a total of 16 mice
Can you see the pattern?
Can you predict what it would be after 12 steps like above?
To find the total number of mice on January 1, 2000, we can break down the problem into several steps:
Step 1: Determine the initial number of mice (on January 1, 1998):
You stated that you bought 2 mice, one male and one female, on January 1, 1998. Therefore, the initial number of mice is 2.
Step 2: Calculate the growth rate:
You mentioned that the female mouse gives birth every two months. So, for every two months, we can assume that the pair of mice will produce one male and one female offspring.
Step 3: Determine the breeding period:
You mentioned that the breeding cycle will continue for two years. Therefore, we need to calculate the number of breeding cycles within this period.
Step 4: Calculate the number of offspring in each breeding cycle:
Considering the information from Step 2, for each breeding cycle (two months), the pair of mice will produce one male and one female offspring.
Step 5: Calculate the total number of mice at the end of the two-year period:
To determine the total number of mice on January 1, 2000, we need to add the initial mice count with the number of offspring produced during each breeding cycle.
Let's perform the calculations:
Step 1: Initial number: 2 mice
Step 2: Growth rate:
Within two months, the pair of mice will produce one male and one female offspring.
Step 3: Breeding period:
The breeding cycle will continue for two years, which is a total of 24 months.
Step 4: Offspring in each breeding cycle:
For each two-month breeding cycle, the pair of mice will produce 1 male and 1 female offspring.
Step 5: Total number of mice at the end of two years (January 1, 2000):
We will calculate the number of offspring in each breeding cycle and add it to the initial number of mice:
Month 0 (January 1, 1998) - Initial count: 2 mice
Month 2 (March 1, 1998) - 2 mice (initial count) + 1 male + 1 female = 4 mice
Month 4 (May 1, 1998) - 4 mice (previous count) + 1 male + 1 female = 6 mice
Month 6 (July 1, 1998) - 6 mice (previous count) + 1 male + 1 female = 8 mice
You can continue this pattern until January 1, 2000 (the end of the two-year period), and add up the counts from each two-month breeding cycle.
By following this method, you'll determine the total number of mice on January 1, 2000.