   Chapter 13.FOM, Problem 4P ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Pollution A chemical plant discharges 2400   tons of pollutants every year into an adjacent lake. Through natural runoff, 70 % of the pollutants contained in the lake at the beginning of the year are expelled by the end of the year.(a) Explain why the following sequence models the amount A n of the pollutant in the lake at the end of the n th   year that the plant is operating. A n = 0.30 a n − 1 + 2400 (b) Find the first five terms of the sequence A n .(c) Find a formula for A n .(d) How much of the pollutant remains in the lake after 6   years ? How much will remain after the plant has been operating a long time?(e) Verify your answer to part (d) by graphing A n with a graphing calculator for n = 1 to n = 20 .

To determine

(a)

To explain:

The sequence models amount An of the pollutant in the lake at the end of the nthyear An=0.30an1+2400

Explanation

Given:

The sequence An=0.30an1+2400.

Approach:

By model theory.

Calculation:

The sequence models amount An of the pollutant in the lake at the end of the nthyear An=0

To determine

(b)

To find:

The first five terms of the sequence An.

To determine

(c)

To find:

A formula for An.

To determine

(d)

To find:

The amount of pollutant that remains in the lake after 6years and after the plant has been operating a long time.

To determine

(e)

To show:

The sequence An by graphing calculator.

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