The following table gives the number of CDs (in millions) sold in the United States for the even-numbered years 1988 through 1996. A plot of these data indicates that CD sales were increasing at a reasonably constant rate over these years.
T (YEAR) | 1988 | 1990 | 1992 | 1994 | 1996 |
S (millions of CDs) | 149.7 | 286.5 | 407.5 | 662.1 | 778.9 |
Source: The World Almanac and Book of Fads 1998 and The World Almanac and Book of Facts 2005.
a. Find the linear model S(t) = at + b that best fits these data.
b. Compare the model's prediction for the year 1995 with the actual 1995 CD sales of 722.9 million.
c. Compare the model's prediction for the year 2002 with the actual 2002 CD sales of 803.3 million.
d. What do you think may have accounted for the discrepancy between the 2002 predicted and actual values?
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