Quantitative Comparisons with Exponents

I got a bunch of good GRE practice on these kinds of questions at work this afternoon. I was sort of blown away by how easy they are, once you think in terms of rewriting the quantities using the rules of exponents and not just freaking out over how the number themselves are huge and a complete pain in the ass to attempt to calculate.

I am quite pleased that an entire section of a chapter in the book, about "applications of linear equations," is set in the microeconomics context - calculating revenues, variable costs, total costs, etc. But I did suggest that given how confusing college students in principles of microeconomics classes and people I have worked with in the past have found these ideas, an introductory section that gives some background information would be helpful. I will definitely get Robert to look at the revised version.

I also suggested changing "that" to "which" in one sentence and my boss (who I will call H, and who is a really nice woman and is the wife of my linear algebra professor) asked me if I could clarify when to use them because she has never been clear on the difference. It was interesting to try to formulate a rule on the fly, since I have long since internalized the distinction so that the application is automatic, but was able to contrast the sentences:

"She has the cup that is blue" - the clause defines something significant about the cup - I am talking about the blue cup and not some other cup - there is an emphasis on the blueness as being important to what I am saying

"She has the cup, which is blue" - the clause merely gives additional information and is not necessary to defining the cup

I learned from H., after a discussion of favorite numbers (yes, everybody had one; math geeks, you know), that the number 4 is considered an unlikely number in Japan (where she is from) because of the similarity of the word for "four" to the word for "death." Wikipedia calls this "tetraphobia" and says that it is a common superstition in East Asia. So would my love for the number four be "tetraphilia"?

Note that today is Friday the 13th. Happy Birthday, Robert! I hope you do not have paraskavedekatriaphobia.