O GRAPHS AND FUNCTIONSApplication problem with a linear function: Finding a coordinate...The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 44 minutes ofcalls is $15.12. and the monthly cost for 58 minutes is $16.38. What is the monthly cost for 53 minutes of calls?Monthly cost(in dollars)Calling time(in minutes)ExplanationCheckO 2021 McGraw Hill LLC. All Rights Reserved. Terms of Use I Privacy Center AccessdtvMacBook Air20 F3F7escF2%232$%II

The monthly cost for 44 minutes of calls is $15.12 and the monthly cost for 58 minutes is $16.38

Answered: Application problem with a linear…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.2: Linear Functions

Problem 2TU

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Manufacturing 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?
Demand for Soft Drinks A convenience stores manager notices that sales of soft drinks 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 95. High temperature Number of cans sold 55 340 58 335 64 410 68 460 70 450 75 610 80 735 84 780
TEST YOUR UNDERSTADING FOR EXAMPLE 3.5 A donation to the university is required for the privilege of purchasing premium season football passes. The cost is a linear function of the number of season passes. It costs 8000 to get season passes for myself and my spouse. To get passes for my entire family of 5, it costs 17,000. Use a formula to express the total cost C, in dollars, of n season passes. EXAMPLE 3.5 CHANGING CELSIUS TO FAHRENHEIT Temperature F=F(C) in Fahrenheit is a linear function of the temperature C in Celsius. A lab assistant placed a Fahrenheit thermometer beside a Celsius thermometer and observed the following: When the Celsius thermometer reads 30 degree (C=30), the Fahrenheit thermometer reads 86 degrees (F=86). When the Celsius thermometer reads 40 degrees, the Fahrenheit thermometer reads 104 degrees. Part 1 Use a formula to express F as a linear function of C. Part 2 At sea level, water boils at 212 degrees Fahrenheit. What temperature in degrees Celsius makes water boil? Part 3 Explain in practical terms what the slope means in this setting.
HOW DO YOU SEE IT? The graphs labeled L1,L2,L3, and L4 represent four different pricing discounts, where p is the original price (in dollars) and S is the sale price (in dollars). Match each function with its graph. Describe the situations in parts c and d. a fp:A50 discount is applied. b gp:A$5 discount is applied. c gfp d fgp
Price of Amazons Kindle The following table shows the price of Amazons Kindle 2 e-book reader. It is adapted from data available on the web. Here time is measured in months since February 2009, when the Kindle was launched. Time Price 0 349 5 299 10 249 15 199 a. By calculating differences, show that these data can be modeled using a linear function. b. Find a linear formula that models these data. Be careful about the sign of the slope. c. What price does your formula from part b project for January 2012 35 months after the Kindle was launched? Note: The web data were the basis for speculation that some day the Kindle would be free.
TEST YOUR UNDERSTADING FOR EXAMPLE 3.3 The State of New York also has an income tax. The tax table for New York shows that a single New York resident with a taxable income of 15,000 owes 671 in New York income tax. If the taxable income is 15,500, then the table shows a tax liability of 701. Assume that the state tax is a linear function of taxable income, and find the tax owed if the taxable income is 15,350. EXAMPLE 3.3 OKLAHOMA INCOME TAX The amount of income tax T=T(l), in dollars, owed to the state of Oklahoma is a linear function of the taxable income l, in dollars, at least over a suitably restricted range of incomes. According to the Oklahoma Income Tax table for the year 2015, a single Oklahoma resident taxpayer with a taxable income of 15,000 owes 579 in Oklahoma income tax. In functional notation, this is T(15,000)=579. If the taxable income is 15,500, then the table shows a tax liability of 605. Part 1 Calculate the rate of change in T with respect to I, and explain in practical terms what it means. Part 2 How much does the taxpayer owe if the taxable income is 15,350?
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.

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