(a)
To calculate: The model of a form
(b)
To graph: The points and graph the model of the form
(c)
The number of Dick’s Sporting Goods stores in the year
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Calculus: An Applied Approach (Providence College: MTH 109)
- Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forwardA regression was run to determine whether there is arelationship between the diameter of a tree (x, in inches) and the tree’s age (y, in years). Theresults of the regression are given below. Use this topredict the age of a tree with diameter 10 inches. y=ax+ba=6.301b=1.044r=0.970arrow_forwardMarginal Tax Rate The following table shows tax due for the given taxable income level for a single taxpayer. Taxable income Tax due 97, 000 21, 913 97, 050 21, 927 97, 100 21, 941 97, 150 21, 955 97, 200 21, 969 a. Show that the data in the table are linear. b. How much additional tax is due on each dollar over 97.000? c. What would you expect to be your tax due if you had a taxable income of 97, 000? of 98, 000? d. Find a linear formula that gives your tax due if your income is A dollars over 97, 000.arrow_forward
- Pharmacology The percent p of prescriptions filled with generic drugs at CVS Pharmacies from 2008 through 2014 (see figure) can be approximated by the model pt=2.77t+45.2,8t111.95t+55.9,12t14 where t represents the year, with t=8 corresponding to 2008. Use this model to find the percent of prescriptions filled with generic drugs in each year from 2008 through 2014.arrow_forwardA regression was run to determine whether there isa relationship between hours of TV watched per day (x) and number of sit-ups a person can do (y). The results of the regression are given below. Use this topredict the number of situps a person who watches 11 hours of TV can do. y=ax+b a=1.341 b=32.234 r=0.896arrow_forwardGrade Point Average In many universities students are given grade points for each credit unit according to the following scale: A 4 points B 3 points C 2 points D 1 point F 0 point For example, a grade of A in a 3-unit course earns 43=12 grade points and a grade of B in a 5-unit course earns 35=15 grade points. A students grade point average GPA for these two courses is the total number of grade points earned divided by the number of units; in this case the GPA is (12+15)8=3.375. a Find a formula for the GPA of a student who earns a grade of A in a units of course work, B in b units, C in c units, D in d units and F in f units. b Find the GPA of a student who has earned a grade of A in two 3-unit courses, B in one 4-unit courses and C in three 3-unit courses.arrow_forward
- XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?arrow_forwardDraw a scatter plot for the data in Table 2. Then determine whether the data appears to belinearly related.arrow_forwardGrade Point Average In many universities students are given grade points for each credit unit according to the following scale: A4 points B3 points C2 points D1 points F0 points For example, a grade of A in a 3-unit earns 43=12 grade points and grade points and a grade of B in a 5-unit course earns 35=15 grade points. A student’s grade point average (GPA) for these two courses is the total number of grade points earned divided by the number of units; in this case the GPA is (12+15)/8=3.375 . (a) Find a formula for a GPA of a student who earns a grade A in a units of course work, B in b units; C in c units, D in d units, and F in f units. (b) Find a GPA of a student who has earned a grade of A in two-units courses. B in one 4-unit course, and C in three 3-unit courses.arrow_forward
- Noise and Intelligibility Audiologists study the intelligibility of spoken sentences under different noise levels. Intelligibility, the MRT score, is measured as the percent of a spoken sentence that the listener can decipher at a cesl4ain noise level in decibels (dB). The table shows the results of one such test. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Find the correlation coefficient. Is a linear model appropriate? (d) Use the linear model in put (b) to estimate the intelligibility of a sentence at a 94-dB noise level.arrow_forwardTEST FOR UNDERSTANDING FOR EXAMPLE 5.16 In the study Economics of Scale in High School Operation by J. Riew, the author studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 enrollment. The data he observed were similar to those in the table below. n=enrollment 200 600 1000 1400 1800 C=costperstudent,indollars 667.4 545.0 461.0 415.4 408.2 Model these data using a quadratic function. Round regression parameters to four decimal places. According to this model, what enrollment produces the minimum cost per student?arrow_forwardMaking Ice Our ice machine is making ice in preparation for the game that starts at 7:00 p.m. The machine is monitored, and the amount of ice is recorded at the end of each hour. The results are in the table below. Time 12:00 p.m. 1:00 p.m. 2:00 p.m. 3:00 p.m. Pounds of ice 200 273 346 419 a. Show that the data are linear. b. Let t denote the time in hours since noon, and let I denote the pounds of ice made. Find a linear model for I as a function of t. c. If 675 pounds of ice will be needed for the game tonight, will the ice machine produce enough ice by game time?arrow_forward
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