Chapter 4.6, Problem 39E

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Depreciation A sports utility vehicle that costs $33,000 new has a book value of$20,856 after 3 years.(a) Find a linear model for the value of the vehicle.(b) Find an exponential model for the value of the vehicle.(c) Find the book values of the vehicle after 1 year and after 4 years using each model.(d) Use a graphing utility to graph the two models in the same viewing window. Which model depreciates faster in the first 3 years?(e) Explain the advantages and disadvantages of using each model to a buyer and to a seller.

(a)

To determine

To calculate: A linear model for the value of the sport utility vehicles that costs $33,000 new has a book value of$20,856 after 3 years.

Explanation

Given Information:

The provide information is that the cost of a new sport utility vehicle is $33,000 which has a book value of$20,856 after 3 years.

Formula used:

The linear cost model is given by the equation,

V=mt+b where V is the value and m is the slope of the model.

Calculation:

Consider the provide information that the cost of a new sport utility vehicle is $33,000 which has a book value of$20,856 after 3 years.

Let the cost of the new vehicle at the time t=0 be $33,000 then the cost at time t=3 is$20,856.

Substitute 0 for t and $33,000 for V in the linear cost value model V=mt+b, 33,000=m(0)+b33,000=b Hence the value of b is$33,000

(b)

To determine

To calculate: A exponential model for the value of the sport utility vehicles that costs $33,000 new has a book value of$20,856 after 3 years.

(c)

To determine

To calculate: The book value of the vehicle after 1 year and after 4 year using linear and exponential model for the value of the sport utility vehicles that costs $33,000 new has a book value of$20,856 after 3 years.

(d)

To determine

To graph: The linear and exponential model calculated in part (a) and part (b) in the same viewing window using a graphing utility provided information that the cost of a new sport utility vehicle is $33,000 which has a book value of$20,856 after 3 years..

(e)

To determine

The advantages and disadvantages of using each linear and exponential model calculated in part (a) and part (b).

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