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Homework Help: Series Help

  1. Dec 9, 2009 #1
    1. The problem statement, all variables and given/known data
    A chemical plant produces pesticide that contains a molecule potentially harmful to people if the concentration is too high. The plant flushes out the tanks containing the pesticide once a week, and the discharge flows into the river. The molecule breaks down gradually in water so that 90% of the amount remaining each week is dissipated by the end of the next week. Suppose that D units of the molecule are discharged each week.

    a) Find the number of units of the molecule in the river after n weeks.
    b) Estimate the amount of the molecule in the water supply over a very long time(hint find the sum of the series)
    c) If the toxic level of the molecule is T units, how large an amount of the molecule can the plant discharge each week?



    3. The attempt at a solution
    A)
    I got a1=D a2=D+.01(D) a3=D+.01(D+.01D)

    so an=D+.01(an-1) or an=a1+.01(an-1)

    B) I'm not sure if I did part b right and I got the sum as n=0 to [tex]\infty[/tex] of a1+.01(an-1) but I have a strong feeling this isn't right.

    C) I don't know what to do for part C
     
  2. jcsd
  3. Dec 10, 2009 #2

    HallsofIvy

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    This is a "recursive" equation but it does not answer the question- you have not yet found a formula for an. You say that a3= D(1+ .01+ .012). Do you see that that is a geometric series? What is the formula for the sum of a finite geometric series?

    Well, what is that sum? What is the formula for the sum of an infinite geometric series?

    For what values of D is the answer to (B) less than T?
     
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