November 2001 Problems

Problem A: Adolescent Pregnancy

You are working temporarily for the Department of Health and Environmental Control. The director is concerned about the issue of teenage pregnancy in their region. You have decided that your team will analyze the situation and determine if it is really a problem in this region. You gather the following 2000 data.

1998

Age          Pregnancies      Births

10-14               320                  231

15-17               4041                3222

18-19               6387                5164

1999

Age             Pregnancies      Births

10-14               309                  208

15-17               3882                3048

18-19               6714                5391

Build a mathematical model and use it to determine if there is a problem or not. Prepare an article for the newspaper that highlights your result in a novel mathematical relationship or comparison that will capture the attention of the youth.

Problem B: Skyscrapers

Skyscrapers vary in height , size (square footage), occupancy rates, and usage. They adorn the skyline of our major cities. But as we have seen several times in history, the height of the building might preclude escape during a catastrophe either human or natural (earthquake, tornado, hurricane, etc). Let's consider the following scenario. A building (a skyscraper) needs to be evacuated. Power has been lost so the elevator banks are inoperative except for use by firefighters and rescue personnel with special keys.

Build a mathematical model to clear the building within X minutes. Use this mathematical model to state the height of the building, maximum occupation, and type of evacuation methods used. Solve your model for X = 15 minutes, 30 minutes, and 60 minutes.