Concept explainers
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
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Reaction rate R |
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a. Use quadratic regression to find a model for the data. Round regression parameters to three decimal places.
b. Use your model to estimate
c. Estimate the concentration at which the reaction rate is
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Reminder 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. Women Employed Outside the Home The following table shows the number, in millions, of women employed outside the home in the given year. Year Number, in millions 1942 16.11 1943 18.70 1944 19.17 1945 19.03 1946 16.78 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 1947, and then estimate that value. c. The actual number of women working outside the home in 1947 was 16.90 million, whereas in 1948 the number was 17.58 million. In light of this, is a quadratic model appropriate for the period from 1942 through 1948?arrow_forwardReminder 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_forward
- Reminder 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_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
- ReminderRound 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_forwardReminder 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. 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_forward
- Reminder Round all answer to two decimal places unless otherwise indicated. Gasoline Prices In 1960, the average price per gallon of gasoline was 31 cents per gallon. Form 1960 to 2000, prices increased, on average, by 2.5 cents per gallon per year. 4 a. Using G for the price, in cents per gallon, and t for the time, in years, since 1960, use a formula to express G as linear function of t. b. What price per gallon does the model yield for 1990? Note: The actual price was 1.00 per gallon. c. Use the Internet to find the average price of gasoline for the current year. Does the model from part a give a price near the current price?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 answer to two decimal places unless otherwise indicated. Budget Constraints Your family likes to eat fruit, but because of budget constraints, you spend only 5 each week on fruit. Your two choices are apples and grapes. Apples cost 1 per pound, and grapes cost 2 per pound. Let a denote the number f pounds of apples you buy and g the number of pounds of grapes. Because of your budget, it is possible to express g as a linear function of the variable a. To find the linear formula, we need to find its slope and initial value. a. If you buy one more pound of apples, how much less money do you have available to spend on grapes? Then how many fewer pounds of grapes can you buy? b. Use your answer to part a to find the slope of g as a linear function of a. Hint: Remember that the slope is the change in the function that results from increasing the variable by 1. Should the slope of g be positive or negative? c. To find the initial value of g, determine how many pounds of grapes you can buy if you buy no apples. d. Use your answer to parts b and c to find a formula for g as a linear function of a.arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning