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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

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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