Concept explainers
Reminder Round all the answers to two decimal places unless otherwise indicated.
Women Employed Outside the Home The following table shows the number, in millions, of women employed outside the home in the given year.
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a. Use regression to find a quadratic model for the data. (Round the regression parameters to three decimal places.)
b. Express using functional notation the number of women working outside the home in
c. The actual number of women working outside the home in
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder Round all answers to two decimal places unless otherwise indicated. Chemical Reaction The following table shows for a certain chemical reaction, the rate of reaction R, in moles per second, as a function of the concentration x, in moles per cubic meter, of the product. Concentration x 10 20 30 40 50 Reaction rate R 18 12 7 3 0 a. Use quadratic regression to find a model for the data. Round regression parameters to three decimal places. b. Use your model to estimate R(24), and explain what your answer means. c. Estimate the concentration at which the reaction rate is 6 moles per cubic meter per second. Consider concentrations only up to a level of 50moles per cubic meter.arrow_forwardReminder Round all the answers to two decimal places unless otherwise indicated. Traffic Accidents The following table shows the rate R of vehicular involvement in traffic accidents per 100,000,000 vehicle-miles as a function of vehicular speed s, in miles per hour, for commercial vehicles driving at night on urban streets. Speed s Accident rate R 20 1600 25 700 30 250 35 300 40 700 45 1300 a. Use regression to find a quadratic model for the data. b. Calculate R(50) and explain what your answer means in practical terms. c. At what speed is vehicular involvement in traffic accidents for commercial vehicles driving at night on urban streets at a minimum?arrow_forwardReminder Round all the answers to two decimal places unless otherwise indicated. Vehicles parked The table shows the number, in thousands, of vehicles parked in the central business district of a certain city on a typical Friday as a function of the hour of the day. Hour of the day Vehicles parked thousands 9 A.M 6.2 11 A.M 7.5 1 P.M 7.6 3 P.M 6.6 5 P.M 3.9 a. Use regression to find a quadratic model for the data. Round the regression parameters to three decimal places. b. Express using functional notation the number of vehicles parked on a typical Friday at 2 P.M., and then estimate that value. c. At what time of day is the number of vehicles parked at its greatest?arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Male and Female High School Graduates The table below shows the percentage of male and female high school graduates who enrolled in college within 12 months of graduation. Years 1960 1965 1970 1975 Males 54 57.3 55.2 52.6 Females 37.9 45.3 48.5 49 a. Find the equation of the regression line for percentage of male high school graduates entering college as a function of time. b. Find the equation of the regression line for percentage of female high school graduates entering college as a function of time. c. Assume that the regression lines you found in part a and part b represent trends in the data. If the trends persisted, when would you expect first to have seen the same percentage of female and male graduates entering college? You may be interested to know that this actually occurred for the first time in 1980. The percentages fluctuated but remained very close during the 1981s and 1990s. In the 2000s, more female graduates entered college than did males. In 2008, for example, the rate for males was 66 compared with 72 for females.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. Cubic Regression Use cubic regression to model the following data. x 2 1 0 1 2 y 1.4 2.7 3.0 2.9 3.0arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. High School GraduatesThe following table shows the number, in millions, graduating from high school in the United States in the given year. Year Number 1975 3.13 1980 3.04 1985 2.68 1990 2.57 1994 2.46 1999 2.76 2004 3.05 2009 3.32 a.Make a plot of the data and explain why a linear model is not appropriate. b.Use regression to find a linear model for the years 1975 through 1990. In this part and the next. round regression line parameters to three decimal places. c.Use regression to find a linear model for the years 1994 through 2009. d.Write a formula for a model of the number, in millions, graduating as a piecewise-defined function using the linear models from part b and part c. e.Make a graph of the formula you found in part d. f.The number graduating in 1995 was 2.52million. On the basis of your graph in part e, determine how this compares with what would be expected from your formula.arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Telecommunications The following table shows the annual expenditures, in dollars, per customer unit for residential landline phone services and cellular phone services in the United States in the given year. Year Landline Cell 2004 592 378 2006 542 524 2008 467 643 2010 401 760 Calculate the regression line for each type of service, and determine expenditure level at which the two line cross. Round your answer for the expenditure level to one decimal place.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. 9. Testing Data for Linearity Consider the following data. x 3 3.3 3.6 3.9 f 8 7.4 6.8 6.2 a. Test the data to see whether they are linear. b. Make a linear model for the data.arrow_forwardReminder Round all answers to two decimal places unless otherwise indicated. High School Graduates The following table shows the number, in millions, graduating from high school in the United States, in the given year. t=Year N= Number graduating 1985 2.83 1987 2.65 1989 2.47 1991 2.29 a. Explain in practical terms what N(1989) means, and find its value. b. Use functional notation to express the number of graduates in 1988, and estimate its value. c. Find the average rate of change per year during the period 1989 to 1991. d. Estimate the value of N(1994).arrow_forward
- Reminder Round all answers to two decimal places unless otherwise indicated. Falling with a Parachute If an average-sized man jumps from an airplane with a properly opening parachute, his downward velocity v=v(t), in feet per second, t seconds into the fall is given by the following table. t=Secondsintothefall v=Velocity 0 0 1 16 2 19.2 3 19.84 4 19.97 a. Explain why you expect v to have a limiting value and what this limiting value represents physically. b. Estimate the terminal velocity of the parachutist.arrow_forwardReminderRound all answers to two decimal places unless otherwise indicated. TargetData from Targets 2014 annual report indicate that the equation of change for the revenue R, in millions of dollars, from 2010 through 2014 is dRdt=1647.7 where t is the time, in years, since 2010. If the initial revenue is 66,726.4 million dollars, find an equation that gives R as a linear function of t.arrow_forwardRemainder Round all answers to two decimal places unless otherwise indicated. Tourism The number, in millions, of international tourists who visited the United States is given in the following table. Date 2010 2011 2012 2013 Millions of tourists 59.74 62.33 66.66 69.77 a.Plot the data. b.Find the equation of the regression line and add its graph to your data plot. Round the regression line parameters to two decimal places. c.Explain in practical terms the meaning of the slope. d.Express, using functional notation, the number of tourists who visited the United States in 2014, and then estimate that value. The actual number was 74.73 million.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning