264 CHAPTER 2 Graphs and Functions 62. Annual Tuition and Fees Refer to the table that accompanies Exercise 61. (a) Use the data points for the years 2013 and 2015 to find a linear equation that models the data. (b) Use the equation from part (a) to estimate average tuition and fees for in-state students at public four-year colleges in 2016. Round to the nearest dollar. How does the result compare to the actual figure given in the table, $8778? 63. Cost of Private College Education The table lists average annual cost (in dollars) of tuition and fees at private four-year colleges for selected years. (a) Determine a linear function ƒ1x2 = ax + b that models the data, where x = 0 represents 2013, x = 1 represents 2014, and so on. Use the points 10, 24,5232 and 14, 29,4782 to graph ƒ and a scatter diagram of the data on the same coordinate axes. What does the slope of the graph indicate? (b) Use the function from part (a) to approximate average tuition and fees, to the nearest dollar, in 2016. Compare the approximation to the actual figure given in the table, $27,942. (c) Use the linear regression feature of a graphing calculator to find the equation of the line of best fit. 64. Distances and Velocities of Galaxies The table lists the distances (in megaparsecs; 1megaparsec = 3.085 * 1024 cm, and 1megaparsec = 3.26 million light-years) and velocities (in kilometers per second) of four galaxies moving rapidly away from Earth. Year Cost (in dollars) 2013 24,523 2014 25,707 2015 26,739 2016 27,942 2017 29,478 Data from National Center for Education Statistics. Galaxy Distance Velocity Virgo 15 1600 Ursa Minor 200 15,000 Corona Borealis 290 24,000 Bootes 520 40,000 Data from Acker, A., and C. Jaschek, Astronomical Methods and Calculations, John Wiley and Sons. Karttunen, H. (editor), Fundamental Astronomy, Springer-Verlag. (a) Plot the data using distances for the x-values and velocities for the y-values. What type of relationship seems to hold between the data? (b) Find a linear equation in the form y = mx that models these data using the points 1520, 40,0002 and 10, 02. Graph the equation with the data on the same coordinate axes. (c) The galaxy Hydra has a velocity of 60,000 km per sec. How far away, to the nearest megaparsec, is it according to the model in part (b)? (d) The value of m is the Hubble constant. The Hubble constant can be used to estimate the age of the universe A (in years) using the formula A = 9.5 * 1011 m . Approximate A using the value of m. Round to the nearest hundredth of a billion years. (e) Astronomers currently place the value of the Hubble constant between 50 and 100. What is the range for the age of the universe A?
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