Concept explainers
(a)
To calculate: A linear function
The graph shows teacher salaries for Nixon country for teachers whose highest degree is a bachelor's degree. Let
(b)
To calculate: The annual salary for a teacher with
(c)
To calculate: The annual salary for a teacher with
(d)
To calculate: The number of years of experience must a teacher have to earn annual salary of
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Intermediate Algebra For College Students (9th Edition)
- 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_forwardAn 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_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_forward
- When Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data are not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of change is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change from 2 to 5 is not the same as the average rate of change from 5 to 6. This shows that the data are not linear, even though the differences in y are constant. x 1 2 5 6 y 3 6 9 12arrow_forwardThe US. import of wine (in hectoliters) for several years is given in Table 5. Determine whether the trend appearslinear. Ifso, and assuming the trend continues, in what year will imports exceed 12,000 hectoliters?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
- When Date Are Unevenly speed. If data are evenly spaced, we need only calculate differences to see whether the data are linear. But if data not evenly spaced, then we must calculate the average rate of change over each interval to see whether the data are linear. If the average rate of changes is constant, it is the slope of the linear function. This fact is used in Exercises 23 and 24. In the following table, show that the average rate of change is the same over each interval. This shows the data are linear, even though the differences in y are not constant. Then find a linear model for the data. x 1 2 5 6 y 7 10 19 22arrow_forwardUse the graph to determine any local maxima or minima.arrow_forwardTable 6 shows the year and the number ofpeople unemployed in a particular city for several years. Determine whether the trend appears linear. If so, and assuming the trend continues, in what year will the number of unemployed reach 5 people?arrow_forward
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