According to the North American Transportation Statistics Database, the total number of vehicle-miles Year | Vehicle Road Miles (in billions) 2000 | 2747 2001 | 2798 2002 | 2856 2003 | 2891 2004 | 2963 2005 | 2989 (a) What variables are appropriate? t (years since 2000) and C (cars on the road in millions) t (years since 2000) and V (vehicle road miles in billions) t (years since 2000) and M (miles driven per day in billions) C (cars on the road in millions) and M (miles driven per day in billions) V (vehicle road miles in billions) and C (cars on the road in millions) (b) Find an equation for a model of these data. (Use the first and second values in the table to calculate) V =
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Step 1:** Identify the two points given in the table: - Point 1: (0, 2747) - Year 2000, Vehicle Road Miles 2747 billion - Point 2: (1, 2798) - Year 2001, Vehicle Road Miles 2798 billion ** Show moreā¦
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Transportation According to data from the Bureau of Trans- portation Statistics, the rate of change in the number of local ransit vehicles (buses, light rail, etc.), in thousands, in the United States from 1970 to the present can be approximated by $$f^{\prime}(t)=4.0674 \times 10^{-4} t(t-1970)^{0.3},$$ where $t$ is the year. Source: National Transportation Statistics $2014 .$ $\begin{array}{l}{\text { (a) Using the fact that in } 1970 \text { there were } 61,298 \text { such ve- }} \\ {\text { hicles, find a formula giving the approximate number of }} \\ {\text { local transit vehicles as a function of time. }} \\ {\text { (b) Use the answer to part (a) to forecast the number of local }} \\ {\text { transit vehicles in the year } 2020 .}\end{array}$
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The number of miles that passenger cars travel annually in the United States is given for selected years. Year Miles (Billions) 1960 0.587, 1965 0.723, 1970 0.917, 1975 1.034, 1980 1.112, 1985 1.247, 1990 1.408, 1996 1.468, 1999 1.569 1. Consider the year as the explanatory (x) variable and miles driven as the response variable (y). Display the scatter plot for the data, does the relationship look linear? 2. Find the regression line for the data with the coefficients to four decimal places. Let X be the year and Y be the number of miles driven (in billions). 3. For each 1 year increase how many more miles are cars expected to drive? Give your answer in billions of miles and round to four decimal places). 4. Based on this data, how many miles are expected to be driven in 2010? Round to two decimal places. 5. Based on the regression line, when will the annual mileage reach 2 billion miles? Report the year in which this happens. 6. When does this line predict that 0 miles will be driven (Report the year in which this is predicted to happen)? Is this prediction problematic? Why?
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