- #1

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 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