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Math1115
Excel computer project #3

Exponential and Logarithmic Function, and Matrices

Goals: The first goal of this project is to introduce students to modeling data using linear regression.
Students will use Excel to fit an exponential and a logarithm model to data, and use the model to
answer questions about the real world situation. Also, students will work with matrices. Students will
discuss how well and to what extent the model describes the situation. The second goal of this
project is to give students hands-on experience using a spreadsheet. Students will plot data, fit a
trend line to the data, and use the “fill” tool to do a calculation repeatedly for a list of data.

Be sure to include your name and identify each problem.

Problem 1: Costco Revenues. The annual revenues R (in millions of dollars) for the Costco
Wholesale Corporation from 1996 to 2005 are shown in the table.

Year Revenue, R Year Revenue, R

1996 19,566 2001 34,797

1997 21,874 2002 38,762

1998 24,270 2003 42,546

1999 27,456 2004 48,107

2000 32,164 2005 52,935

a. Create a spreadsheet in worksheet with the above data and appropriate column headings.

Title the Worksheet “Costco Revenues from 1996 to 2005”.

b. Create a scatter plot of the data. Let x represent the number of years from 1990 and y equal
to the annual revenues in millions of dollars. (x = 6 corresponding to 1996). The table should
be titled “Annual Costco Revenues”. The axis labels should be “Revenue in Millions of Dollars”
and “Years 1996 to 2005”.

c. Add an Exponential Trend line and its equation to the scatter plot.

d. Add a Logarithmic Trend line and its equation to the scatter plot.

ANSWER THE FOLLOWING QUESTIONS ON A SEPARATE SHEET OF PAPER:

1. What is the Exponential Trend line model equation?

2. What is the Logarithmic Trend line model equation?

3. How well do the Exponential and the Logarithmic models fit the data? Which is a better fit?

4. Use the two models to predict the revenues in 2006 and in 2007. It is projected that revenues
in 2006 and 2007 will be $59,050 million and $64,500 million, respectively. Do the predictions
from the two models agree with these projections? Explain.

5. Use the two models to predict revenues in 2009, 2010, and 2011. It is projected that revenue

will reach $81,000 million during the period from 2009 to 2011. Does the prediction from each
model agree with the projection? Explain.

Problem 2: Restaurants. The total sales y (in billions of dollars) for fast-food and full-service
restaurants for the years 1999 to 2005 are shown in the table.

Year Fast-food Full-service

1999 103.0 125.4

2000 107.1 133.8

2001 111.6 139.9

2002 115.1 141.9

2003 120.5 148.3

2004 129.4 157.0

2005 135.6 164.9

a. Create a spreadsheet in worksheet with the above data and appropriate column headings.
Title the Worksheet “Restaurant Sales from 1999 to 2005”.

b. Create a scatter plot of the data for fast-food sales. Let x represent year from 1990 (x = 9
corresponding to 1999) and y equal to Fast-Food Sales. The table should be titled “Restaurant
Sales for Fast Food vs. Full Service”. The axis labels should be “Sales in Billions of Dollars”
and “Years 1996 to 2005”.

c. On the same scatter plot, create a scatter plot for Full-service sales.

d. Add a trend line for Fast-food sales and its equation.

e. Add a trend line for Full-service sales and its equation.

ANSWER THE FOLLOWING QUESTIONS ON A SEPARATE SHEET OF PAPER:

1. What is the Trend line equation for the Fast-food model?

2. What is the Trend line equation for the Full-service model?

3. Assuming that the amounts for the given 7 years are representative of future years; will fast-
food sales ever equal full-service sales? Explain.