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

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 2 years ago

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