Concept explainers
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated.
Magnitude and Distance Astronomers measure brightness of stars using both the absolute magnitude, a measure of the true brightness of the star, and the apparent magnitude, a measure of the brightness of a star as it appears from Earth. The difference between apparent and absolute magnitude should yield information about the distance to the star. The following table gives magnitude difference
Star | Magnitude difference
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Distance
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Algol |
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Aldebaran |
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Capella |
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Canopus |
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Pollux |
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Regulus |
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a. Plot
b. Give an exponential model for the data.
c. If one star shows a magnitude difference
d. Alphecca shows a magnitude difference of
e. Alderamin is
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Atmospheric Pressure The table below gives a measurement of atmospheric pressure, in grams per square centimeter, at the given altitude, in kilometers. Altitude Atmospheric Pressure 5 569 10 313 15 172 20 95 25 52 For comparison, 1 kilometer is about 0.6 mile, and 1 gram per square centimeter is about 2 pounds per square foot. a.Plot the data on atmospheric pressure. b.Make an exponential model for the data on atmospheric pressure. c.What is the atmospheric pressure at an altitude of 30 kilometers? d.Find the atmospheric pressure on Earths surface. This is termed standard atmospheric pressure. e.At what altitude is the atmospheric pressure equal to 25 of standard atmospheric pressure?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Choose the Model A car travels down a straight highway at a constant speed. Which is a better model for the distance traveled as a function of the time: linear or exponential?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Traffic in the Lincoln TunnelCharacteristics of traffic flow include density D, which is the number of cars per mile, and average speed s in milesperhour.Traffic system engineers have investigated several methods for relating density to average speed. One study considered traffic flow in the north tube of the Lincoln Tunnel and fitted an exponential function to observed data. Those data are partially presented in the table below. Speed s Density D 32 34 25 53 20 74 17 88 13 102 a.Make an approximate exponential model of D as a function of s. b.Express, using functional notation, the density of traffic flow when the average speed is 28mileperhour, and then calculate that density. c.If average speed increases by 1mileperhour, what can be said about density?arrow_forward
- Remainder 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_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places but round all other answers to two decimal places unless otherwise indicated. Grazing Rabbits The amount A of vegetation measured in pounds eaten in a day by a grazing animal is a function of the amount V of food available measured in pounds per acre. Even if vegetation is abundant, there is a limit, called the satiation level, to the amount the animal will eat. The following table shows, for rabbits, the difference D between the satiation level and the amount A of food eaten for a variety of values of V. V=vegetaionlevel D=satiationlevel-A 27 0.16 36 0.12 89 0.07 134 0.05 245 0.01 a.Draw a plot of D versus V. b.Find an exponential function that approximates D. c.The satiation level of a rabbit is 0.18 pound per day. Use this, together with your work in part b, to find a formula for A. d.Find the vegetation level V for which the amount of food eaten by the rabbit will be 90 of its satiation level of 0.18 pound per day.arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. National Health Care SpendingThe following table shows national health care costs, measured in billions of dollars. Date 1970 1980 1990 2000 2010 Costs, in billions 75 253 714 1353 2570 a.Plot the data. b.Find an exponential function that approximates the data for health care costs. c.By what percentage per year were national health care costs increasing during the period from 1970 through 2010? d.Use functional notation to express how much money was spent on health care in the year 2011, and then estimate that value.arrow_forward
- Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Gray Wolves in WisconsinGray wolves were among the first mammals protected under the Endangered Species Act in the 1970s. Wolves recolonized in Wisconsin beginning in 1980.Their population grew reliably after 1985 as follows: Year Wolves Year Wolves 1985 15 1993 40 1986 16 1994 57 1987 18 1995 83 1988 28 1996 99 1989 31 1997 145 1990 34 1998 178 1991 40 1999 197 1992 45 2000 266 a. Explain why an exponential model may be appropriate. b. Are these data exactly exponential? Explain. c. Find an exponential model for these data. d. Plot the data and the exponential model. e. Comment on your graph in part d. Which data points are below or above the number predicted by the exponential model?arrow_forwardSpecial Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Growth in Length of HaddockA study by Raitt showed that the maximum length that a haddock could be expected to grow is about 53centimeters.Let D=D(t) denote the difference between 53centimeters and the length at age t years. The table below gives experimentally collected values for D. Age t Difference D 2 28.2 5 16.1 7 9.5 13 3.3 19 1.0 a.Find an exponential model of D as a function of t. b.Let L=L(t) denote the length in centimeters of a haddock at age t years. Find the model for L as a function of t. c.Plot the graph of the experimentally gathered data for the length L at ages 2,5,7,13, and 19years along with the graph of the model you made for L. Does this graph show that the 5year old haddock is a bit shorter or a bit longer than would be expected? d.A fisherman has caught a haddock that measures 41centimeters. What is the approximate age of the haddock?arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Postal RatesThe table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States tyears after 1900. t=time,inyearssince1900 s=costofstamp 19 2 32 3 58 4 71 8 78 15 85 22 95 32 102 37 109 44 116 47 a.Use exponential regression to model s as an exponential function of t. b.What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. The actual cost was 25cents. c.Plot the data and the exponential model.arrow_forward
- Special Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Caloric Content Versus Shell Length In 1965, Robert T.Paine gathered data on the length L, in millimeters, of the shell and the caloric content C, in calories, for a certain mollusk. The table below is adapted from those data. L=length C=Calories 7.5 92 13 210 20 625 24 1035 31 1480 a.Find an exponential model of calories as a function of length. b.Plot the graph of the data and the exponential model. Which of the data points show a good deal less caloric content than the model would predict for the given length? c.If length is increased by 1millimeter, how is caloric content affected?arrow_forwardSpecial Rounding Instructions When you perform logistic regression, round the r value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless other-wise indicated. Magazine Sales Our new magazine initially sells 300 copies per month. Research indicates that a vigorous advertising campaign could increase sales by 20 each month if our market were unlimited. But research also indicates that magazine sales in our area are unlikely to exceed 1200 per month. Make a logistic model of projected magazine sales.arrow_forwardSpecial Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Cell phones The following table shows the number, in millions, of cell phone subscribers in the United States at the end of the given year. Year Subscribersmillions 2010 296.3 2011 316.0 2012 326.5 2013 335.6 2014 355.4 a.Plot the data points. b.Use exponential regression to construct an exponential model for the subscriber data. c.Add the graph of the exponential model to the plot in part a. d.What was the yearly percentage growth rate from the end of 2010 through the end of 2014 for cell phone subscribership? e.In 2014, an executive had a plan that could make money for the company, provided that there would be at least 380million cell phone subscribers by the end of 2016. Solely on the basis of an exponential model for the data in the table, would it be reasonable for the executive to implement the plan?arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning