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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

Depreciation A construction company purchases a bulldozer for $ 160 , 000 . Each year the value of the bulldozer depreciates by 20% of its value in the preceding year. Let V n be the value of the bulldozer in the n th year. (Let n = 1 be the year the bulldozer is purchased.)

( a ) Find a formula for V n .

( b ) In what year will the value of the bulldozer be less than $ 100 , 000 ?

To determine

(a)

To find:

A formula for Vn.

Explanation

Given:

a=160,000 and depreciation=0.20.

Approach:

The nth term of a geometric sequence is given by

an=arn1

where a is the first term and r is the common ratio of the sequence.

Calculation:

The value of the bulldozer in the next year after depreciation will be 80% of its value in the preceding year

To determine

(b)

To find:

The year when the value of the bulldozer is less than $100,000.

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