I. Starbucks Stores (Modeling) We all know that the number of Starbucks stores increased rapidly during 1992–2009. To see how rapidly, observe the following table, which gives the number of U.S. stores and the total number of stores during this period. Year Number of U.S. Stores Total Stores 1992 113 127 1993 163 183 1994 264 300 1995 430 483 1996 663 746 1997 974 1121 1998 1321 1568 1999 1657 2028 2000 2119 2674 2001 2925 3817 2002 3756 5104 2003 4453 6193 2004 5452 7567 2005 7353 10,241 2006 8896 12,440 2007 10,684 15,011 2008 11,567 16,680 2009 11,128 16,635 To investigate how the number of stores is likely to increase in the future and how the total number of stores compares with the number of U.S. stores, complete the following. 1. Create a scatter plot of the points (x, f (x)), with x equal to the number of the years past 1990 and f (x) equal to the number of U.S. stores in the designated year. 2. Find an exponential function that models these data. Rewrite the function with base e. 3. How accurately does this model estimate the number of U.S. stores in 2000 and in 2006? 4. Find a logistic function that models the data. Does this model estimate the number of U.S. stores in 2000 and in 2006 better than the exponential model? 5. Graph the exponential model and the logistic model on the same axes as the scatter plot to determine whether the exponential or the logarithmic model is the better fit.
I. Starbucks Stores (Modeling)
We all know that the number of Starbucks stores increased rapidly during 1992–2009. To see how rapidly, observe the following table, which gives the number of U.S. stores and the total number of stores during this period.
|
Year |
Number of U.S. Stores |
Total Stores |
|
1992 |
113 |
127 |
|
1993 |
163 |
183 |
|
1994 |
264 |
300 |
|
1995 |
430 |
483 |
|
1996 |
663 |
746 |
|
1997 |
974 |
1121 |
|
1998 |
1321 |
1568 |
|
1999 |
1657 |
2028 |
|
2000 |
2119 |
2674 |
|
2001 |
2925 |
3817 |
|
2002 |
3756 |
5104 |
|
2003 |
4453 |
6193 |
|
2004 |
5452 |
7567 |
|
2005 |
7353 |
10,241 |
|
2006 |
8896 |
12,440 |
|
2007 |
10,684 |
15,011 |
|
2008 |
11,567 |
16,680 |
|
2009 |
11,128 |
16,635 |
To investigate how the number of stores is likely to increase in the future and how the total number of stores compares with the number of U.S. stores, complete the following.
1. Create a
2. Find an exponential
3. How accurately does this model estimate the number of U.S. stores in 2000 and in 2006?
4. Find a logistic function that models the data. Does this model estimate the number of U.S. stores in 2000 and in 2006 better than the exponential model?
5. Graph the exponential model and the logistic model on the same axes as the scatter plot to determine whether the exponential or the logarithmic model is the better fit.
I really need question 5 please!
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