The monetary value of a certain antique chair increases with its age (but at a diminishing rate). The rate of change in the value of the chair can be modeled as 2200 v(x) = x1.5 dollars per year where x years is the age of the chair, x 2 25. The chair was valued at $200 twenty-five years after it was crafted. (For the following questions, disregard inflation of the dollar.) (a) How much will the value of the antique increase between 25 and 100 years after it was crafted? How much will it be worth 100 years after it was crafted?

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.7: Direct And Inverse Variation
Problem 36PS
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The monetary value of a certain antique chair increases with its age (but at a diminishing rate). The rate of change in the value of the chair can be modeled as
2200
v(x) =
x1.5
dollars per year
where x years is the age of the chair, x 2 25. The chair was valued at $200 twenty-five years after it was crafted. (For the following questions, disregard inflation of the dollar.)
(a) How much will the value of the antique increase between 25 and 100 years after it was crafted?
How much will it be worth 100 years after it was crafted?
$4
(b) How much will the chair eventually be worth? Use the algebraic method.
$
Transcribed Image Text:The monetary value of a certain antique chair increases with its age (but at a diminishing rate). The rate of change in the value of the chair can be modeled as 2200 v(x) = x1.5 dollars per year where x years is the age of the chair, x 2 25. The chair was valued at $200 twenty-five years after it was crafted. (For the following questions, disregard inflation of the dollar.) (a) How much will the value of the antique increase between 25 and 100 years after it was crafted? How much will it be worth 100 years after it was crafted? $4 (b) How much will the chair eventually be worth? Use the algebraic method. $
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