Question

Problem:: The number of Starbucks stores grew after they first opened. The number of stores from 1990-2011, as reported on their corporate website is shown in the chart below..

Carefully plot the data. You should be able to see that the data is NOT linear, but actually exponential.

Year	Number of Starbucks stores	Year	Number of Starbucks stores
1990	84	2001	4709
1991	116	2002	5886
1992	165	2003	7225
1993	272	2004	8569
1994	425	2005	10241
1995	677	2006	12440
1996	1015	2007	15011
1997	1412	2008	16680
1998	1886	2009	16635
1999	2498	2010	16858
2000	3501	2011	17003

Turn in the following

Your graph showing the data plotted (should be curved)

Problem 2::A new truck costs $32000. The truck's value depreciates over time,which means it loses value.For tax purposes depreciation is calculated linearly. So V (current value) is equal to the P (original price) - n (years) times x (depreciation value). V = P - nx....If the truck is worth $24,500 after three years, find the depreciation value constant x. Now use that to write a formula write a general formula for the value (V) after n years. Your equation will only have n and V as variables. Using that formula find the value of this truck after 10 years. Find the age of the truck when the value is $0.

Turn in the following

1. value of X (depreciation constant)

2. general formula with V and n as variables

3. value of truck after 10 years

4. age of the truck when its value is zero.

Answer 1

1) from the graph we can see the number of starbucks varies exponentially with the year.

V=P-nx ....1(1)

where V =current worth of truck

P= original price

n= number of years

x=depreciation value

a) truck is worth 24500$ after 3 years

so applying equation (1)

24500=32000- 3*x

x=(32000-24500)/3

=2500 ( depriciation constant)

b) now putting x in equation (1)

V=P-2500n general formula

c) value of truck after 10 years

V=p-nx=32000- 10*(2500)

=7000

d)age of truck when its value is zero( V=0)

0= 32000- n(2500)

n=(32000)/2500

=12.8 year (approximately 13 years)