Question
In a pest eradication program, "N" sterilized male flies are released into a general population each day.
It is estimated that 90% of these flies will survive a give data.
A) Show that the number of sterilzed flies in population "n" days after the program begun is:
N+(0.9)N+N(0.9)^2+N(0.9)^3+......+N(0.9)^(n-1),
(geometric sequence)
B) If long range goal of the program is to keep 20,000 sterilized male flies in the population, how many flies should be released each day?
It is estimated that 90% of these flies will survive a give data.
A) Show that the number of sterilzed flies in population "n" days after the program begun is:
N+(0.9)N+N(0.9)^2+N(0.9)^3+......+N(0.9)^(n-1),
(geometric sequence)
B) If long range goal of the program is to keep 20,000 sterilized male flies in the population, how many flies should be released each day?
Answers
Steve
A) just check the population after each day
1: 90% survive; a new batch is added.
Total is .90N+N
2: 90% of 1st day's group survive: .90*.90
90% of 2nd batch survive; N more added
total: .90*.90N + .90N + N
So, after n days, you can see the proposed sequence.
B) You want the limit to be 20000, so
N/(1-.90) = 20000
N =200,000
1: 90% survive; a new batch is added.
Total is .90N+N
2: 90% of 1st day's group survive: .90*.90
90% of 2nd batch survive; N more added
total: .90*.90N + .90N + N
So, after n days, you can see the proposed sequence.
B) You want the limit to be 20000, so
N/(1-.90) = 20000
N =200,000