Algebra and Maths

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?

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  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

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