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Imuell1
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Homework Statement
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?
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