A factory installs new machinery that saves S(x) = 1600 − 60x dollars per year, where x is the number of years since installation. However, the cost of maintaining the new machinery is C(x) = 100x dollars per year. a) Find the year x at which the maintenance cost C(x) will equal the savings S(x). (At this time, the new machinery should be replaced. Round your answer to the nearest whole number.) x=__________ years b) Find the accumulated net savings (in dollars) [savings S(x) minus cost C(x)] during the period from t = 0 to the replacement time found in part (a). (Round your answer to the nearest whole number.)
A factory installs new machinery that saves S(x) = 1600 − 60x dollars per year, where x is the number of years since installation. However, the cost of maintaining the new machinery is C(x) = 100x dollars per year. a) Find the year x at which the maintenance cost C(x) will equal the savings S(x). (At this time, the new machinery should be replaced. Round your answer to the nearest whole number.) x=__________ years b) Find the accumulated net savings (in dollars) [savings S(x) minus cost C(x)] during the period from t = 0 to the replacement time found in part (a). (Round your answer to the nearest whole number.)
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter12: Quadratic Functions
Section12.6: Solving Problems Involving Quadratic Equations
Problem 1.1E
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
A factory installs new machinery that saves
S(x) = 1600 − 60x dollars per year, where x is the number of years since installation. However, the cost of maintaining the new machinery is
C(x) = 100x dollars per year.
a) Find the year x at which the maintenance cost C(x) will equal the savings
S(x). (At this time, the new machinery should be replaced. Round your answer to the nearest whole number.)
x=__________ years
b) Find the accumulated net savings (in dollars) [savings
S(x) minus cost C(x)] during the period from t = 0 to the replacement time found in part (a). (Round your answer to the nearest whole number.)
$___________
Transcribed Image Text:y
$ per year
savings
S= 1600 - 60 x
1600
net
savings
cost
C = 100 x
Year
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning