Question

In: Math

Year/Number of Years Since 1971/Number of stores 1971    0 1 1987 16 17 1988 17...

Year/Number of Years Since 1971/Number of stores

1971   

0

1

1987

16

17

1988

17

33

1989

18

55

1990

19

84

1991

20

116

1992

21

165

1993

22

272

1994

23

425

1995

24

677

1996

25

1015

1997

26

1412

1998

27

1886

1999

28

2498

2000

29

3501

2001

30

4709

2002

31

5886

2003

32

7225

2004

33

8569

2005

34

10241

2006

35

12440

2007

36

15011

2008

37

16680

2009

38

16635

2010

39

16858

2011

40

17003

2012

41

18066

2013

42

19767

2014

43

21366

2015

44

22519
  • Identify the initial value and the growth rate of your exponential model and explain what they mean in the context of Starbucks Stores. Put your explanations in a text box.
  • Use your exponential model to predict the number of Starbucks locations in the following years:

1980, 1990, 2000, 2010, 2020, 2030, 2040, 2050

Solutions

Expert Solution

Year No. of years since 1971, X No. of stores Log Transformed Y
1987 16 17 2.833213344
1988 17 33 3.496507561
1989 18 55 4.007333185
1990 19 84 4.430816799
1991 20 116 4.753590191
1992 21 165 5.105945474
1993 22 272 5.605802066
1994 23 425 6.052089169
1995 24 677 6.517671273
1996 25 1015 6.922643891
1997 26 1412 7.252762418
1998 27 1886 7.542213463
1999 28 2498 7.823245691
2000 29 3501 8.160803921
2001 30 4709 8.45723085
2002 31 5886 8.680331929
2003 32 7225 8.885302513
2004 33 8569 9.055906319
2005 34 10241 9.23415455
2006 35 12440 9.428672366
2007 36 15011 9.616538545
2008 37 16680 9.721965676
2009 38 16635 9.719264188
2010 39 16858 9.732580601
2011 40 17003 9.741145078
2012 41 18066 9.801786998
2013 42 19767 9.89176916
2014 43 21366 9.969556153
2015 44 22519 10.02211468

After Regressing ln(y) on x:

ln(y) = 0.122 + 0.252*x

y =

= 1.13*

Initial Value:

When x = 0

y = 1.13

Growth Rate is: 0.252

Interpretation:

Initial value: These are the number of stores present at time t= 0.

Growth Rate: Stores are increasing at an exponential rate of 0.252/yr

Year Year Since 1971 Predicted Stores
1980 9 10.91586933
1990 19 135.6689372
2000 29 1686.1745
2010 39 20956.78277
2020 49 260463.4004
2030 59 3237194.549
2040 69 40233785.37
2050 79 500049490.6

milcah answered 1 year ago
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