Concept explainers
Straight-line Depreciation Suppose that a company has just purchased a new machine for its manufacturing facility for . The company chooses to depreciate the machine using the straight-line method over 10 years.
a. Write a linear model that expresses the book value of the machine as a function of its age .
b. What is the implied domain of the function found in part (a)?
c. Graph the linear function.
d. What is the book value of the machine after 4 years?
e. When will the machine have a book value of ?
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Precalculus Enhanced with Graphing Utilities, Books a la Carte Edition Plus NEW MyLab Math -- Access Card Package (7th Edition)
Additional Math Textbook Solutions
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus (10th Edition)
Glencoe Math Accelerated, Student Edition
University Calculus: Early Transcendentals (4th Edition)
Calculus: Early Transcendentals (2nd Edition)
Calculus: Early Transcendentals (3rd Edition)
- An outpatient operating room charges each patient a fixed amount per surgery plus an amount per minute for use. One patient was charged 250 for a 30-minute surgery and another patient was charged 450 for a 90-minute surgery. Determine the linear function that would be used to compute the charges. Use the function to determine the charge when a patient has a 45-minute surgery.arrow_forwardManufacturing Cost The manager of a furniture factory finds that it costs 2200 to produce 100 chairs in one day and 4800 to produce 300 chairs in one day. a Assuming that the relationship between cost and the number of chairs produced is linear, find a linear function C that models the cost of producing x chairs in one day. b Draw a graph of C. What is the slope of this line? c At what rate does the factorys cost increase for every additional chair produced?arrow_forwardDemand for Soft Drinks A convenience store manager notices that sales of soft drink are higher on hotter days, so he assembles the data in the table. (a) Make a scatter plot of the data. (b) Find and graph a linear function that models the data. (c) Use the model to predict soft drink sales if the temperature is 95Farrow_forward
- High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number graduating in millions 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. By calculating difference, show that these data can be modeled using a linear function. b. What is the slope for the linear function modeling high school graduations? Explain in practical terms the meaning of the slope. c. Find a formula for a linear function that models these data. d. Express, using functional notation, the number graduating from high school in 1994, and then use your formula from part c to calculate that value.arrow_forwardTuition at American Public Universities This is a continuation of Exercise 6. The following table shows the average yearly in-state tuition and required fees, in dollars, charged by four-year American public universities in the school year ending in the given year. Date Average tuition 2012 8318 2013 8595 2014 8872 2015 9149 2016 9426 a. Show that these data can be modeled by a linear function, and find its formula. b. What is the slope for the linear function modeling tuition and required fees for public universities? c. What is the slope of the linear function modeling tuition and required fees for private universities? Note: See Exercise 6. d. Explain what the information in parts b and c tells you about the rate of increase in tuition in public versus private institutions. e. Which type of institution shows the larger percentage increase from 2015 to 2016? 6. Tuition at American Private Universities The following table shows the average yearly tuition and required fees, in dollars, charged by four-year American private nonprofit universities in the school year ending in the given year. Date Average tuition 2012 27, 870 2013 29, 004 2014 30, 138 2015 31, 272 2016 32, 406 a. Show that these data can be modeled by a linear function, and find its formula. b. Plot the data points and add the graph of the linear formula you found in part a. c. What prediction does this formula give for average tuition and fees at four-year American private nonprofit universities for the academic year ending in 2021?arrow_forwardA phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $10 andthen a certain amount of money per megabyte (MB)of data used on the phone. If a customer uses 20 MB,the monthly cost will be $11.20. Ifthe customer uses130 MB, the monthly cost will be $1180. a. Find a linear equation for the monthly cost of thedata plan as a function of x, the number of MB used. b. Interpret the slope and y-intercept of the equation. c. Use your equation to find the total monthly cost if 250 MB are used.arrow_forward
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningIntermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning