math

Homework 4

1. We often predict the future based on past events. Here are two different studies that try to predict what course of action to take by looking at past results. Read about both studies and then answer the questions that follow.

The Situations Situation 1

Susanna is having a hard time getting an apartment outside of the dorms. She has interviewed with several groups, but not been chosen. Most of the interviews are after dinner. She asked around and found several people who recently had interviewed for apartments and been accepted. They all had a sandwich for dinner with some kind of soda. Susanna plans to stop at Subway before her next interview for a sandwich and a soda.

Situation 2

Dr. DeGraves is working in a large clinic. He recently read a research report with a large database that listed a number of conditions and the habits of patients who had those conditions. He noticed that most of the patients with high cholesterol drank coffee and did not exercise. He planned to advise his next patient with high cholesterol to stop drinking coffee and to get plenty of exercise.

The Questions

a. State how the methods used in these two situations are the same and how

they are different.

b. Write about what you think can be concluded in each case. Is the data in either situation useful? If so, how and why? If not, why not?

c. How could the research methods that were used be improved?

2. Stacking Cups. Your friend’s boss manufactures Styrofoam cups and has given your friend the assignment of determining the height for a box that will hold a stack of 100 cups. Your friend has a few of the cups, but he has no idea of how he can figure out the height of a stack of 100 of them.

He has started measuring stacks of cups. He has measured one cup and found that it was 3½ inches high. Two cups are 4 inches high, and three cups are 4 ½ inches high.

a. Make a table with at least five entries to show your friend how to organize the data.

b. Draw a graph to show how the height is increasing as the number of cups increases.

c. Write an equation to represent the problem for any number of cups.

d. For each representation a-c, explain to your friend how he or she could use it to find the height of 100 cups.

e. Which method, a, b, or c, would you recommend to your friend for future use and why?