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.
First Down The following table shows the probability
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a. Use exponential regression to model the data.
b. Plot the data along with the exponential model.
c. What probability does the model give of gaining a first down for fourth down and
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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. 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_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. 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 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_forward
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- 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. Medicare ExpendituresThe following table is from the Centers for Medicare that is, M=1000?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. Rare Coins The table below shows the estimated value C, in dollars, of an 1877 Indian Head Cent Philadelphia mint mark in very fine condition t years after 1950. t=time,inyearssince1950 C=value,indollars 0 25 30 400 45 625 54 1750 60 2000 a.Use exponential regression to model C as an exponential function of t. b.According to your exponential model, by what percentage does the value of the 1877 cent increase from year to year?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. 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_forward
- A local real estate agent argues that house prices in Pittsburgh are related tothe number of rooms in a house. You collect a random sample of 190 houses and run asimple regression using House Price (measured in dollars) as the dependent variableand Rooms (measured as the number of rooms in a house) as the independentvariable. Given below is the Excel output of the regression results. (a) Construct the 99.7% confidence interval for the slope of the regressionline.(b) Consider a house with 5 room. What is the probability that the housewill sell for more than $270,245?(c) A savvy real estate investor, Noah, owns a house in Pittsburgh thathe is planning to sell. Based on the regression put, Noah decides to destroy somewalls to reduce the number of rooms in the house, hoping to increase the houseselling price. Based on the regression output, do you think this is a good decision?Justify your comment.arrow_forward1a) Compare the kurtosis of the two distributions and interpret it. 1b) What is the z-score for a man whose life expectancy is 80? 1c) Based on this, in what percentile would this man be for life expectancy? 1d) What is the raw score for a man in the 37th percentile? 1e) What area, or proportion, of the population has a lower life expectancy? 1f) Interpret the meaning of the proportion of the calculation from 1c.arrow_forwardA random sample of college students were surveyed about technological devices. They were asked, “How many cell phone chargers do you have in your household?” The table below represents the probability density function for the random variable X, the number of cell phone chargers per household. Find the standard deviation of X. Round the final answer to two decimal places. x P(X = x) 4 1/4 5 1/4 9 1/2arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill