Remainder Round all answers to two decimal places unless otherwise indicated.
Running Ants A scientist collected the following data on the speed, in centimeters per second, at which ants ran at the given ambient temperature, in degrees Celsius.
Temperature | Speed |
25.6 | 2.62 |
27.5 | 3.03 |
30.3 | 3.57 |
30.4 | 3.56 |
32.2 | 4.03 |
33.0 | 4.17 |
33.8 | 4.32 |
a. Find the equation of the regression line, giving the speed as a function of the temperature.
b. Explain in practical terms the meaning of the slope of the regression line.
c. Express, using functional notation, the speed at which the ants run when the ambient temperature is 29 degrees Celsius, and then estimate that value.
d. The scientist observes the ants running at a speed of 2.5 centimeters per second. What is the ambient temperature?
Trending nowThis is a popular solution!
Chapter 3 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Remainder Round all answers to two decimal places unless otherwise indicated. Cost of Employee Replacement The table next page shows the percentage P of an employees annual salary S, in thousands of dollars, spent on the process of recruiting and training a replacement. S = annual salary thousands of dollars P= percentage of salary for recruiting 20 515 30 15 40 20 60 45 70 50 a.Plot the data points. b.Find the equation of the regression line. c.Add the plot of the regression line to the data from part a. d.What cost does the regression line give for replacement of an employee who makes an annual salary of 50, 000?arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. 4. Facebook Users in Australia The following table shows both current and projected data on the number, in millions, of Facebook users in Australia. t = years since 2012 F = number of Facebook users millions 0 9.2 1 10.0 2 10.8 3 11.7 4 12.6 5 13.2 6 13.8 a.Plot the data. b.Find the equation of regression line, and add its graph to the plot from part a. c.Explain in practical terms the meaning of the slope of the regression line.arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. Domestic Auto Sales in the United States For 2005 through 2008, the following table shows the total U.S. sales, in millions, of domestic automobiles excluding light trucks. Date Domestic cars sold 2005 5.53 2006 5.48 2007 5.25 2008 4.54 a.Get the equation of the regression line rounding parameters to two decimal places, and explain in practical terms the meaning of the slope. In particular, comment on the meaning of the sign of the slope. b.Plot the data points and the regression line. c.In 2009, 3.62 million domestic cars were sold in the United States. How does the forecast obtained from the regression line compare with this figure?arrow_forward
- Remainder Round all answers to two decimal places unless otherwise indicated. 2. Federal Methamphetamine Arrests The table below shows the number A, in thousands, of federal arrests for methamphetamine t years after 2006. t = years since 2006 A= thousands of arrests 0 5.85 1 5.54 2 4.72 3 4.70 Find the equation of the regression line for A as a function of t.arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. Cell Phones The following table gives the amount spent on cellular service worldwide, in trillions of U.S. dollars. Round the regression parameters to three decimal places. Date Cellular service revenue 2011 1.01 2012 1.05 2013 1.09 2014 1.11 a.Plot the data points. b.Find the equation of the regression line and add its graph to the plotted data. c.In 2015, 1.14 trillion was spent on cellular service. If you had been a financial strategist in 2014 with only the data in the table above available, what would been your prediction for the amount spent on cellular service in 2015?arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. 6. iPhone Sales The following table shows unit sales of iPhones for the given year. t= years since 2010 0 1 2 3 I= units sold millions 8.70 16.24 37.04 47.79 a.Find the equation of the regression line. b.Plot the data and the regression line on the same coordinate axes. c.How many units sold does the regression line predict for 2016? d.Use the Internet to find the number of iPhones actually sold in 2016, and compare that number with your answer to part c.arrow_forward
- Remainder Round all answers to two decimal places unless otherwise indicated. Gross Domestic Product U.S. gross domestic product, in trillions of dollars, is given in the table below. Date Gross domestic product 2010 15.0 2011 15.5 2012 16.2 2013 16.7 a.Find the equation of the regression line, and explain the meaning of its slope. Round regression line parameters to two decimal places. b.Plot the data points and the regression line. c.When would you predict that a gross domestic product of 17.3 trillion dollars would be reached? The actual gross domestic product in 2014 was 17.3 trillion dollars. What does that say about your prediction?arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. Long Jump The following table shows the length, in meters, of the winning long jump in the Olympic Games for the indicated year. One meter is 39.37 inches. Year 1900 1904 1908 1912 Length 7.19 7.34 7.48 7.60 a.Find the equation of the regression that gives the length as a function of time. Round the regression line parameters to three decimal places. b.Explain in practical terms the meaning of the slope of the regression line. c.Plot the data points and the regression line. d.Would you expect the regression line formula to be a good model of the winning length over a long period of time? Be sure to explain your reasoning. e.There were no Olympic Games in 1916 because of World War I, but the winning long jump in the 1920 Olympic Games was 7.15 meters. Compare this with the value that the regression line model gives. Is the result consistent with your answer to part d?arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. Driving You are driving on a highway. The following table gives your speed S, in miles per hour, as a function of the time t, in seconds, since you started making your observations. Time t 0 15 30 45 60 Speed S 54 59 63 66 68 a.Find the equation of the regression that expresses S as a linear function of t. b.Explain in practical terms the meaning of the slope of the regression line. c.On the basis of the regression line model, when do you predict that your speed will reach 70 miles per hour? Round your answer to the nearest second. d.Plot the data points and the regression line. e.Use your plot in part d to answer the following: Is your prediction in part c likely to give a time earlier or later than the actual time when y our speed reaches 70 miles per hour?arrow_forward
- Remainder Round all answers to two decimal places unless otherwise indicated. Motor Vehicle Fatalities The table below shows the traffic fatality rate R, in fatalities per 100 million vehicle miles travelled, t years after 2010. Find the equation of the regression line for R as a function of t. t = years since 2010 R = rate 0 1.11 1 1.10 2 1.14 3 1.09 4 1.07arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. 7. DirecTV Subscribers The table on the next page shows the number S, in millions, of subscribers to DirecTV t years after 1995. t = years since 1995 S = subscribers, in millions 0 1.20 4 6.68 7 11.18 9 13.00 16 19.89 19 20.35 a.Find the equation of the regression line for S as a function of t. b.What number does this equation give for DirecTV subscribers in 2013? The actual number was 20.25 million. c.Explain in practical terms the meaning the meaning of the slope of the line you found in part a. d.Plot the data points and the regression line.arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. Is a Linear Model Appropriate? The number, in thousands, of bacteria in a petri dish is given by the following table. Time is measured in hours. Time in hours since experiment began Number of bacteria in thousands 0 1.2 1 2.4 2 4.8 3 9.6 4 19.2 5 38.4 6 76.8 The table below shows enrollment, in millions of people, in private colleges in the United States during the years from 2004 through 2008. Date Enrollment in millions 2004 4.29 2005 4.47 2006 4.58 2007 4.76 2008 5.13 a.Plot the data points for number of bacteria. Does it look reasonable to approximate these data with a straight line? b.Plot the data points for college enrollment. Does it look reasonable to approximate these data with a straight line?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning