Series & Sequences: Understanding N Flies & Population Control

[regnar]

I don't understand anything about this question:

In a pest eradication program, N sterilized male flies are released into the general population each day, and 90% of these flies will survive a given day.

A) Show that the number of sterilized flies in the population after n days is
N + (.9)N + (.9)²N + ... + (.9)^n-1N​

B) If the long ranger goal (infinite) of the program is to keep 20,000 sterilized males in the population, how many such flies should be released each day?​

 

[HallsofIvy]

What is your question? What have you done on this and where did you have problems?

 

[gomunkul51]

Try to build a series that simulates the expression in your problem !
May be try a geometric series, its easy to work with and the big plus is that you know the sum of this series.

 

[hunt_mat]

Let's look at the first few terms.

At the start of the first day there are N flies, that the end of the first day there are $$0.1N$$ flies left.

At the start of the second day there will be 0.1N+N=1.1N flies. At the end of the second day there will be 10% of these left = 0.1*(1.1N)=0.11N flies.

At the start of the third day there will be 0.11N+N=1.11N flies. At the end of the third day there will be 10% of these left = 0.1*(1.11N)=0.111N flies.

Can you see where this is going? This is a geometric series.