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?

Answer 1

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