On February 3, 2008 the New York Giants beat the New England Patriots in Super Bowl XLII held in Glendale, Arizona. The website azsuperbowl.com gives some information about the economic impact that the Super Bowl might have on the local economy. Specifically, we learn that

• during Super Bowl XLII, University of Phoenix Stadium is projected to seat 73,000 people. Past host cities and the NFL estimate that an additional 50,000 non-game ticket holders visit Super Bowl cities each year to be a part of the festivities;

• the average Super Bowl attendee spends four nights in a hotel. Of the attendees, 85% are from another state, 70-90% arrive by plane and the average fan spends $1,500 - $2,000 during his/her stay;

• the average economic impact of the Super Bowl on a host city is $300-400 million.

Use this information and your knowledge of sequences and series to answer the following questions.

Please work with pencil and paper to record your thinking and results.

1. If the average fan spends $1,500 during his/her stay, use the information given to give the total

amount of money that will be spent by those visiting Arizona for Super Bowl XLII.

2. Of the total money spent locally during Super Bowl XLII, a certain percentage will be re-spent and

provide an additional boost to the local economy. Suppose 40% of the money is re-spent, then 40% of

that amount is re-spent, etc. This pattern continues indefinitely. What was the total impact, in dollars,

on the local Arizona economy considering how the money was re-spent locally?

3. Now suppose 65% of the money is re-spent, then 65% of that amount is re-spent, etc. This pattern

continues indefinitely. What was the total impact, in dollars, on the local Arizona economy considering

how the money was re-spent locally?

4. Suppose r% of the money is re-spent, then r% of that amount is re-spent, etc. This pattern continues

indefinitely. Write a function, S(r), that gives the total impact, in dollars, on the local Arizona economy

considering how the money was re-spent locally.

5. Graph the function from #4. Describe the behavior of the function as increases.

6. The website azsuperbowl.com predicts that the total economic impact locally from Super Bowl XLII

will be between $300 million and $400 million. What percentage of the money spent on Super Bowl

XLII was re-spent (and then re-spent again, etc.) to product a total economic impact of $300 million?

What about $400 million?