Search Site



Advanced Search


 

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.

County

Age

10-14

Pregnant

Age 15-17

Pregnant

Age 18- 19

Pregnant

10-14 births

15-17

births

18-19

births

10-14

births-unmarried

15-17 birth-

unmarried

18-19

births-unmarried

1

29

350

571

17

281

437

16

164

193

2

24

303

567

13

206

466

13

151

233

3

40

422

691

29

307

546

28

251

366

4

21

201

356

18

184

326

15

137

180

5

16

156

357

11

109

254

10

99

161

6

44

523

970

33

442

803

32

293

396

7

17

263

434

9

201

345

7

113

168

8

23

330

427

16

256

444

14

160

210

9

13

123

221

10

113

199

9

78

106

10

41

467

950

24

446

686

22

279

331

11

28

421

713

18

343

615

15

219

328

12

9

179

311

8

145

261

7

114

162

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.