The average number N (in thousands) of daily newspapers in circulation in the United States from 2000 through 2014 can be approximated by the model N = 56,146 − 314.980t3/2, 0 ( t ( 14, where t represents the year, with t = 0 corresponding to 2000. The table shows the average daily number of newspapers for selected years.
Year __________ Newspapers, N
2000 ..................... 55,773
2002 ..................... 55,186
2004 ..................... 54,626
2006 ..................... 52,329
2008 ..................... 48,597
2010 ..................... 44,100
2012 ..................... 43,433
2014 ..................... 40,420
(a) Use a graphing utility to plot the data and graph the model in the same viewing window. How well does the model fit the data?
(b) Use the graph in part (a) to estimate the year in which there was an average of 50,000,000 daily newspapers in circulation.
(c) Use the model to verify algebraically the estimate from part (b)?