Concept explainers
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
EXAMPLE 3.3 OKLAHOMA INCOME TAX
The amount of income tax
Part 1 Calculate the rate of change in
Part 2 How much does the taxpayer owe if the taxable income is
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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- Tuition 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_forwardDemand 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 780arrow_forward6. 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_forward
- 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.arrow_forwardDropping Rocks on Mars The behavior of objects falling near Earths surface depends on the mass of Earth. On Mars, a much smaller planet than Earth, things are different. If Galileo had performed his experiment on Mars, he would have obtained the following table of data. t = seconds V = feet per second 0 0 1 12.16 2 24.32 3 36.48 4 48.64 5 60.8 a. Show that these data can be modeled by a linear function, and find a formula for the function. b. Calculate V10 and explain in practical terms what your answer means. c. Galileo found that the acceleration due to gravity of an object falling near Earths surface was 32 feet per second per second. Physicists normally denote this number by the letter g. If Galileo had lived on Mars, what value would he have found for g?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 chair in or day. (a) Assuming that the relationship between cost and the number of chair’ produced is linear, find a linear function C that models the cost of producing x chair’s in one day. (b) Draw a graph of C. What is the slope of this line? (c) At what rate does the factory’s cost increase for every additional chair produced?arrow_forward
- Later High School Graduates This is a continuation of Exercise 16. 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 2001 2.85 2003 2.98 2005 3.11 2007 3.24 a. Find the slope of the linear function modeling high school graduations, and explain in practical terms the meaning of the slope. b. Find a formula for a linear function that models these data. c. Express, using functional notation, the number graduating from high school in 2008, and then calculate the value. d. The actual number graduating from high school in 1994 was about 2.52 million. Compare this with the value given by the formula in part b and with your answer to part of Exercise 16. Which is closer to the actual value? In general terms, what was the trend in high school graduations from 1985 to 2007? 16. High School Graduates The following table shows the number, in millions, graduating from high school in the United States in the given year.16 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_forwardWorking on a Commission A certain man works in sales and earns a base salary of 1000 per month plus 5 of his total sales for the month. a. Explain why his total monthly income I is a linear function of total sales S, both measured in dollars. b. How much does he earn if he sells 1600 in merchandise in a month? c. Write a formula that gives total monthly income as a linear function of sales in a month. d. What should his monthly total sales be if he wishes to earn 1350 this month?arrow_forward
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