(adsbygoogle = window.adsbygoogle || []).push({}); 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 thatDunits of the molecule are discharged each week.

a) Find the number of units of the molecule in the river afternweeks.

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 a_{1}=D a_{2}=D+.01(D) a_{3}=D+.01(D+.01D)

so a_{n}=D+.01(a_{n-1}) or a_{n}=a_{1}+.01(a_{n-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 a_{1}+.01(a_{n-1}) but I have a strong feeling this isn't right.

C) I don't know what to do for part C

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# Series Help

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