Use exponential regression to fit the data set. (Round your answers to three decimal places.) X X = y 1 53 2 3 4 5 55.2 57.4 59.7 62 Give the exponential model. O y = 45.91 x 0.62* O y = 61.21 x 1.25* y = 51.01 x 1.04* O y = 71.41 x 0.73* O y = 35.71 x 1.46* Use the model found above to calculate y(2.9). y(2.9)=-46.26 Solve y = 64 for x. = (2273) 2.9=51.61 x -51.01 -51.01 -48.11 = 1.04*
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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?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. 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?Cable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?
- Special 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. Fluorescent Bulbs Compact fluorescent light bulbs save energy when compared with traditional incandescent bulbs. Our green energy campaign includes efforts to get local residents to exchange their incandescent bulbs fur fluorescent bulbs. Initially 200 households make the change. Market studies suggest that, in the absence of limiting factors, we could increase that number by 25 each month. In our target area, there are 250,000 households, which we take as the limiting value. Make a logistic model that gives the number of households converting to fluorescent bulbs after t months.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. Household IncomeThe following table shows the median income, in thousands of dollars, of American families for 2003 through 2008. Year Incomethousands of dollars 2003 52.68 2004 54.06 2005 56.19 2006 58.41 2007 61.36 2008 61.52 a.Plot the data. b.Use exponential regression to construct an exponential model for the income data. c.What was the yearly percentage growth rate in median family income during this period? d.From 2003 through 2008, inflation was about 3 per year. Did median family income keep pace with inflation during this period?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. 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?
- 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. Cost of Scientific periodicals The table below shows the average cost C, in dollars, of chemistry and physics periodicals tyears after 1980. 29 t=yearssince1980 C=cost,indollars 0 140 5 250 10 410 15 780 20 1300 22 1520 a.Make an exponential model of C as a function of t. b.Plot the data and the exponential model. c.What was the yearly percentage growth rate of the cost of chemistry and physics periodicals? d.If this exponential trend continues, what will be the expected average cost of physics and chemistry periodicals in 2020? Round your answer to the nearest dollar.Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.Special 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. Natural Gas Production The following table shows natural gas production N in trillions of cubic feet in the United states t years after 1940. t=yearssince1940 N=cubicft.intrilliions 0 3.75 10 8.48 20 15.09 30 23.79 40 21.87 50 21.52 60 24.15 a. Make a logistic model for N as a function of t. b. Graph the data and the logistic model. c. Which years production was farthest from the prediction of the logistic model? d. What does the logistic model predict for the amount of natural gas that will be produced in the long run? Note: In other contexts, this would be known as the carrying capacity..
- Special 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. PTA Participation A school board has a plan to increase participation in the PTA. Currently only about 25 parents attend meetings. Suppose the school board plan results in logistic growth of attendance. The school board believes that its plan can eventually lead to an attendance level of 50 parents. In the absence of limiting factors, the school board believes that its plan can increase participation by 10 each month. Let m denote the number of months since the participation plan was put in place, and let P be the number of parents attending PTA meetings. a. What is the carrying capacity K for a logistic model of P versus m? b. Find the constant b for a logistic model. c. Find the r value for a logistic model. Round your answer to three decimal places. d. Find a logistic model for P versus m.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 P, as a percentage, of a college football team converting on fourth down when not goal to go versus the distance D, in yards, to the first down maker. 28 D = distance, in yards P = probability 1 70 2 60 3 53 4 46 5 41 6 37 7 34 8 32 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 10yards to go? Note: the actual probability is 28.Special 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. An Epidemic In a city of half a million, there are initially 800 cases of a particularly virulent strain of flu. The Centers for Disease Control and Prevention in Atlanta claims that the cumulative number of infections with this flu strain will increase by 40 per week if there are no limiting factors. Make a logistic model of the potential cumulative number of cases of flu as a function of weeks from initial outbreak, and determine how long it will be before 100, 000 people are infected.