Question

Population Growth and Value Decline

Mini-projects are designed to critically stretch your thinking, let you explore the concept, or make you look at a specific situation or related problem. By nature, they are more difficult than the regular exercises.

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

value of X (depreciation constant)

general formula with V and n as variables

value of truck after 10 years

age of the truck when its value is zero.

Turn in typed by an attachment by the due date in the class schedule.

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Answer 1

Problem 1

Graph showing exponential increase in number of startbucks stores

Problem 2

Given :

Price of New truck P = 32,000

Price after 3 years V = 24,500

Using Equation:

V = P – nx

24500 = 32000 – 3x

3x = 7500

x = 2500

Therefore, the value of the depreciation constant is 2500

Equation => V = 32000 – 2500n

a) Value of truck after 10 years

Using this equation to calculate the value of the truck after 10 years (i.e. n = 10)

 V = 32000 – 2500 * (10)

 V = 7000

Value of truck after 10 years is $7,000

b) Age of the truck when value is $0

Using this equation to calculate n when V = 0

 0 = 32000 – 2500n

 n = 12.8

Value of the truck is $0 after 12.8 years