**IFSC 4399/5399 Information, the future and fun things like that**

**Homework 2, due Wednesday, Sept. 9**

M Sept. 7 is a holiday.

Please check over this assignment early, and let me know if you would like us to go over in class how to do any of these, or have any other questions.

1. Consider the different methods of making predictions that we went over in class. Pick the topic of your choice, apply them to that topic, and make some predictions about the future. You may focus on one scenario, or discuss alternative scenarios as well. You may write speculatively, or ground your discussion in facts and examples found on the Web or elsewhere. If purely speculatively without hunting down data on the Web, then more writing would make sense than if much of your time was spent finding data. A variation to a purely speculative essay would be to couch it as a short story, like a science fiction story. Alternatively, you can write a computer program that makes predictions, for example using the exponential curve equation or some other approach. In this vein, you could use Excel or another spreadsheet program to extrapolate. If you want to do something like that but aren't sure how, let me know and we can discuss in class how to use spreadsheets this way.

2. Recall the discussion of exponential curves. Using a spreadsheet or calculator, estimate the following (some hints follow, if you get stuck). Put the answers on your blog, but if the spreadsheets do not upload easily, it is not necessary to upload the actual spreadsheets.

Estimate the doubling time of the software development productivity of the average programmer, if productivity increases at 6%/year.

Estimate the percent per year of increases in the complexity of PC computers if this complexity doubles every 2 years. (By "complexity" we could say we're talking about the number of transistors on a CPU chip, if you were wondering.)

Estimate the percent per year of increases in the complexity of PC computers if complexity doubles every 18 months, as some think it is doing.

What is the doubling time of your money if you have it in the bank making 2% interest per year?

**Hints**

Here are some HW hints that many of you might find of interest. We can talk more about it on Monday if people wish.

A student asks:

Q: I figured out the estimation with interest in the bank, but I did not use a formula. Did we need to have a formula? I just made up an amount of money to start off with. But I was not sure if there was a specific amount that you wanted.

Answer: Just calculating the results, one year at a time, is the easiest way to do it. Any amount of money to start with should give the same answer in number of years.

HW: Estimate the doubling time of the software development productivity of the average programmer, if productivity increases at 6%/year.

Q: Is there a number that I start off with?

Answer: I would suggest starting with any number, then add 6% each year until it is double. The number of years it takes is the answer. Let's suppose current programmer productivity is 1000. Then the next year, it would be 1000 plus 6% of 1000. 6% is the same as 6/100 (definition of "%"). So we need to find 1000+(6/100)*1000. That equals 1.06*1000, which works out to 1060 after the first year.

Estimate the percent per year of increases in the complexity of PC computers if this complexity doubles every 2 years. (By "complexity" we could say we're talking about the number of transistors on a CPU chip, if you were wondering.)

HW: Estimate the percent per year of increases in the complexity of PC computers if complexity doubles every 18 months, as some think it is doing.

Q: And although it may be simple, I am not sure how to figure out the percent per year. How do I do that?

Answer: Trial and error! For a doubling in 2 years, plug in, say 40% and run your year-by-year calculation twice, for the two years, and see if the result is a doubling. If it more than doubles, try 39%. If it less than doubles, try 41% instead.For doubling in 18 months, that is the same as quadrupling in 3 years. With a whole number of years, you can now just run your year-by-year calculation 3 times, for the 3 years.

## No comments:

## Post a Comment

(Anyone may comment)