Superlesson
Project 12-2
Advanced Algebra
Chapter 12, Discrete Mathematics and
Models
In the following activities, you will use recursion to explore
changes in real estate prices and geometrical patterns.
Part A, Recursive Sequences
1. Use the Median
Sale Price Web site to answer the following questions.
a. Find the table of median sale prices of existing single-family homes. Record the average single-family home selling prices for 1996 and 1997.
b. Find the percent change in average selling prices to the nearest hundredth.
c. Suppose you purchased a single-family home in 1996 at the average selling price for that year, that the value of the house changes at the rate you calculated in (1b), and that, each year, you make improvements that increase the value of your property by $3000. Give the value of the house in 1997, 1998, and 1999.
d. Define a recursive sequence that gives Vn, the value of your property n years after purchase.
e. Give an explicit formula for the recursive sequence you have defined.
f. Find the value of your house after 10 years. By how much has the value increased over the purchase price?
g. How long will it take for the value of your house to double?
Part C, Making Connections
2. Find the grid for John
Conway's game of Life.
a. Click on "the rules" to review the rules of the game. Then go to the Game of Life home page. Under "The Game," choose the initial generation called "Cross" and click on "initial generation".
b. How many generations does it take for the cross pattern to become stable? Sketch the stable pattern.
c. How many generations does it take for the "Diagonal Egg" to become stable? Why does the pattern have this property?
d. Describe the life cycle of the "Glider." Why do you think it is called the "Glider"?
e. Start with a blank grid. Design a pattern, with at least 5 occupied cells, that dies after one generation.
f. Start with a blank grid. Design a pattern, with at least 5 occupied cells, that is stable.