COS 109: Problem Set 1

Tue Sep 20 09:09:39 EDT 2016

Due 5:00 PM, Tuesday Sept 26, on paper, in class, or in the box outside my office (Room 419, 4rd floor, CS building).

Collaboration policy for COS 109: Working together to really understand the material in problem sets and labs is encouraged, but once you have things figured out, you must part company and compose your written answers independently. That helps you to be sure that you understand the material, and it obviates questions of whether the collaboration was too close.

You must list any other class members with whom you collaborated.

Problem set answers need not be long, merely clear enough that we can understand what you have done, though for computational problems, show enough of your work that we can see where your answer came from. There is no need to repeat the question, and it saves paper if you just give the answers. PLEASE submit typed material, not hand-written, and keep a copy for yourself in case something goes astray. Thanks.

Do not use Google or other search engines for these questions. Your task is to work from what you know (or observe about your own behavior) and can reason about, not what you can look up.

1. Technology Usage

For a 4 hour period this week, record your technology usage. You will want to choose a four hour period which you consider typical for the week, so not a period when you are sleeping :-) or a period when you are attending class, ... but rather a period you feel accurately represents your use of technology.

Include in your record, the usage of all technologies --

For each of these devices, record the following:

  1. What kind of application you used -- e.g voice, messaging, word processing, e-mail, web
  2. What hardware (cell phone, PC, etc.) and software (e.g. Chrome browser, facebook app, Word, etc. ) platform you used it on. Also differentiate between programs running in a browser and apps that have been downloaded
  3. When and how long you used it

You will want to record your usage at certain intervals during this period, perhaps stopping every hour to record usage.

2. Estimation and quantitative reasoning

In this exercise, you are to estimate any quantities whose values you need to complete the exercise. You will be judged not on the precision of your answers but rather on the steps in your process and the manner in which you justify the assumptions you are making.

(a) Using the results of your technology log, estimate how many hours you will use each form of technology during the course of your 4 years at Princeton. Explain the assumptions you have made in extending the results from a 4 hour measurement to your 4 years at Princeton.

(b) Assuming your technology log is typical for Princeton students, estimate how many hours Princeton students spend in a year using each form of technology. Explain the assumption you have made in deriving this result.

(c) Extend your results from part (b) to estimate how many hours all college students in the country spend in a year using each form of technology. Again, explain the assumptions you have made in deriving this result.

(d) Using your answer from part (c), make the radical assumption that all college students decide to forgo technology for a year intending to use the time that they would use on all forms of technology to walk. Based on your answer to part (c), how many miles will be walked?

(e) How many trips back and forth from Princeton to your hometown does the distance given in (d) represent? You will want to tell us your home town and your estimate of the distance from Princeton there in explaining your answer.

3. Pure estimation

In class, we estimated the number of gas stations in America to be on the order of 100,000. Here we will extend that process to further estimate other quantities.

(a) How many gallons of gas are sold in a typical day. You may wish to recreate some of the discussion in class to generate an estimate here. Feel free to do so, but be sure to explain the logic you used in deriving your result.

(b) Based on your answer to (a), estimate how much money is spent on gas each day.

(c) A gallon of gas weighs 6.3 pounds and the average tax per gallon sold (this varies by the state) is about 50 cents per gallon sold. Using these numbers, estimate the weight of gasoline sold in a year and the amount of tax collected on annual gasoline sales.